Search results for: τ1τ2-regular generalized star closed sets
889 Solution of Nonlinear Second-Order Pantograph Equations via Differential Transformation Method
Authors: Nemat Abazari, Reza Abazari
Abstract:
In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.
Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2569888 Public Transport Planning System by Dijkstra Algorithm: Case Study Bangkok Metropolitan Area
Authors: Pimploi Tirastittam, Phutthiwat Waiyawuththanapoom
Abstract:
Nowadays the promotion of the public transportation system in the Bangkok Metropolitan Area is increased such as the “Free Bus for Thai Citizen” Campaign and the prospect of the several MRT routes to increase the convenient and comfortable to the Bangkok Metropolitan area citizens. But citizens do not make full use of them it because the citizens are lack of the data and information and also the confident to the public transportation system of Thailand especially in the time and safety aspects. This research is the Public Transport Planning System by Dijkstra Algorithm: Case Study Bangkok Metropolitan Area by focusing on buses, BTS and MRT schedules/routes to give the most information to passengers. They can choose the way and the routes easily by using Dijkstra STAR Algorithm of Graph Theory which also shows the fare of the trip. This Application was evaluated by 30 normal users to find the mean and standard deviation of the developed system. Results of the evaluation showed that system is at a good level of satisfaction (4.20 and 0.40). From these results we can conclude that the system can be used properly and effectively according to the objective.
Keywords: Dijkstra Algorithm, Graph Theory, Shortest Route, Public Transport, Bangkok Metropolitan Area.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6338887 Determination of Adequate Fuzzy Inequalities for their Usage in Fuzzy Query Languages
Authors: Marcel Shirvanian, Wolfram Lippe
Abstract:
Although the usefulness of fuzzy databases has been pointed out in several works, they are not fully developed in numerous domains. A task that is mostly disregarded and which is the topic of this paper is the determination of suitable inequalities for fuzzy sets in fuzzy query languages. This paper examines which kinds of fuzzy inequalities exist at all. Afterwards, different procedures are presented that appear theoretically appropriate. By being applied to various examples, their strengths and weaknesses are revealed. Furthermore, an algorithm for an efficient computation of the selected fuzzy inequality is shown.Keywords: Fuzzy Databases, Fuzzy Inequalities, Fuzzy QueryLanguages, Fuzzy Ranking.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1375886 Best Co-approximation and Best Simultaneous Co-approximation in Fuzzy Normed Spaces
Authors: J. Kavikumar, N. S. Manian, M.B.K. Moorthy
Abstract:
The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.
Keywords: Fuzzy best co-approximation, fuzzy quotient spaces, proximinality, Chebyshevity, best simultaneous co-approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1617885 A New Model for Discovering XML Association Rules from XML Documents
Authors: R. AliMohammadzadeh, M. Rahgozar, A. Zarnani
Abstract:
The inherent flexibilities of XML in both structure and semantics makes mining from XML data a complex task with more challenges compared to traditional association rule mining in relational databases. In this paper, we propose a new model for the effective extraction of generalized association rules form a XML document collection. We directly use frequent subtree mining techniques in the discovery process and do not ignore the tree structure of data in the final rules. The frequent subtrees based on the user provided support are split to complement subtrees to form the rules. We explain our model within multi-steps from data preparation to rule generation.Keywords: XML, Data Mining, Association Rule Mining.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1631884 EEG Waves Classifier using Wavelet Transform and Fourier Transform
Authors: Maan M. Shaker
Abstract:
The electroencephalograph (EEG) signal is one of the most widely signal used in the bioinformatics field due to its rich information about human tasks. In this work EEG waves classification is achieved using the Discrete Wavelet Transform DWT with Fast Fourier Transform (FFT) by adopting the normalized EEG data. The DWT is used as a classifier of the EEG wave's frequencies, while FFT is implemented to visualize the EEG waves in multi-resolution of DWT. Several real EEG data sets (real EEG data for both normal and abnormal persons) have been tested and the results improve the validity of the proposed technique.Keywords: Bioinformatics, DWT, EEG waves, FFT.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5562883 Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching
Authors: Xia Zhou, Shouming Zhong
Abstract:
The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.
Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1570882 Self-adaptation of Ontologies to Folksonomies in Semantic Web
Authors: Francisco Echarte, José Javier Astrain, Alberto Córdoba, Jesús Villadangos
Abstract:
Ontologies and tagging systems are two different ways to organize the knowledge present in the current Web. In this paper we propose a simple method to model folksonomies, as tagging systems, with ontologies. We show the scalability of the method using real data sets. The modeling method is composed of a generic ontology that represents any folksonomy and an algorithm to transform the information contained in folksonomies to the generic ontology. The method allows representing folksonomies at any instant of time.
Keywords: Folksonomies, ontologies, OWL, semantic web.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1630881 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method
Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin
Abstract:
This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.
Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1930880 Power Minimization in Decode-and-XOR-Forward Two-Way Relay Networks
Authors: Dong-Woo Lim, Chang-Jae Chun, Hyung-Myung Kim
Abstract:
We consider a two-way relay network where two sources exchange information. A relay helps the two sources exchange information using the decode-and-XOR-forward protocol. We investigate the power minimization problem with minimum rate constraints. The system needs two time slots and in each time slot the required rate pair should be achievable. The power consumption is minimized in each time slot and we obtained the closed form solution. The simulation results confirm that the proposed power allocation scheme consumes lower total power than the conventional schemes.
Keywords: Decode-and-XOR-forward, power minimization, two-way relay
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1589879 Nullity of t-Tupple Graphs
Authors: Khidir R. Sharaf, Didar A. Ali
Abstract:
The nullity η(G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f(w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced subgraph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the endvertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs,
Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.
Keywords: Graph theory, Graph spectra, Nullity of graphs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1918878 An Optimized Design of Non-uniform Filterbank
Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena
Abstract:
The tree structured approach of non-uniform filterbank (NUFB) is normally used in perfect reconstruction (PR). The PR is not always feasible due to certain limitations, i.e, constraints in selecting design parameters, design complexity and some times output is severely affected by aliasing error if necessary and sufficient conditions of PR is not satisfied perfectly. Therefore, there has been generalized interest of researchers to go for near perfect reconstruction (NPR). In this proposed work, an optimized tree structure technique is used for the design of NPR non-uniform filterbank. Window functions of Blackman family are used to design the prototype FIR filter. A single variable linear optimization is used to minimize the amplitude distortion. The main feature of the proposed design is its simplicity with linear phase property.Keywords: Tree structure, NUFB, QMF, NPR.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1739877 Terminal Wiener Index for Graph Structures
Authors: J. Baskar Babujee, J. Senbagamalar,
Abstract:
The topological distance between a pair of vertices i and j, which is denoted by d(vi, vj), is the number of edges of the shortest path joining i and j. The Wiener index W(G) is the sum of distances between all pairs of vertices of a graph G. W(G) = i Keywords:
Graph,
Degree,
Distance,
Pendent vertex,
Wiener index,
Tree.
876 Statistical Properties and Performance of Ecological Indices Based On Relative Abundances
Authors: Gebriel M. Shamia
Abstract:
The Improved Generalized Diversity Index (IGDI) has been proposed as a tool that can be used to identify areas that have high conservation value and measure the ecological condition of an area. IGDI is based on the species relative abundances. This paper is concerned with particular attention is given to comparisons involving the MacArthur model of species abundances. The properties and performance of various species indices were assessed. Both IGDI and species richness increased with sampling area according to a power function. IGDI were also found to be acceptable ecological indicators of conditions and consistently outperformed coefficient of conservatism indices.Keywords: Statistical ecology, MacArthur model, Functional Diversity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2030875 Random Subspace Neural Classifier for Meteor Recognition in the Night Sky
Authors: Carlos Vera, Tetyana Baydyk, Ernst Kussul, Graciela Velasco, Miguel Aparicio
Abstract:
This article describes the Random Subspace Neural Classifier (RSC) for the recognition of meteors in the night sky. We used images of meteors entering the atmosphere at night between 8:00 p.m.-5: 00 a.m. The objective of this project is to classify meteor and star images (with stars as the image background). The monitoring of the sky and the classification of meteors are made for future applications by scientists. The image database was collected from different websites. We worked with RGB-type images with dimensions of 220x220 pixels stored in the BitMap Protocol (BMP) format. Subsequent window scanning and processing were carried out for each image. The scan window where the characteristics were extracted had the size of 20x20 pixels with a scanning step size of 10 pixels. Brightness, contrast and contour orientation histograms were used as inputs for the RSC. The RSC worked with two classes and classified into: 1) with meteors and 2) without meteors. Different tests were carried out by varying the number of training cycles and the number of images for training and recognition. The percentage error for the neural classifier was calculated. The results show a good RSC classifier response with 89% correct recognition. The results of these experiments are presented and discussed.
Keywords: Contour orientation histogram, meteors, night sky, RSC neural classifier, stars.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 411874 Optimization of the Aerodynamic Performances of an Unmanned Aerial Vehicle
Authors: Fares Senouci, Bachir Imine
Abstract:
This document provides numerical and experimental optimization of the aerodynamic performance of a drone equipped with three types of horizontal stabilizer. To build this optimal configuration, an experimental and numerical study was conducted on three parameters: the geometry of the stabilizer (horizontal form or reverse V form), the position of the horizontal stabilizer (up or down), and the landing gear position (closed or open). The results show that up-stabilizer position with respect to the horizontal plane of the fuselage provides better aerodynamic performance, and that the landing gear increases the lift in the zone of stability, that is to say where the flow is not separated.
Keywords: Aerodynamics, wind tunnel, turbulence model, lift, drag.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1274873 Order Penetration Point Location using Fuzzy Quadratic Programming
Authors: Hamed Rafiei, Masoud Rabbani
Abstract:
This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1602872 WAF: an Interface Web Agent Framework
Authors: Xizhi Li, Qinming He
Abstract:
A trend in agent community or enterprises is that they are shifting from closed to open architectures composed of a large number of autonomous agents. One of its implications could be that interface agent framework is getting more important in multi-agent system (MAS); so that systems constructed for different application domains could share a common understanding in human computer interface (HCI) methods, as well as human-agent and agent-agent interfaces. However, interface agent framework usually receives less attention than other aspects of MAS. In this paper, we will propose an interface web agent framework which is based on our former project called WAF and a Distributed HCI template. A group of new functionalities and implications will be discussed, such as web agent presentation, off-line agent reference, reconfigurable activation map of agents, etc. Their enabling techniques and current standards (e.g. existing ontological framework) are also suggested and shown by examples from our own implementation in WAF.Keywords: HCI, Interface agent, MAS.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1660871 A Nonconforming Mixed Finite Element Method for Semilinear Pseudo-Hyperbolic Partial Integro-Differential Equations
Authors: Jingbo Yang, Hong Li, Yang Liu, Siriguleng He
Abstract:
In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.
Keywords: Pseudo-hyperbolic partial integro-differential equations, Nonconforming mixed element method, Semilinear, Error estimates.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1641870 The Countabilities of Soft Topological Spaces
Authors: Weijian Rong
Abstract:
Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft first-countable spaces, soft second-countable spaces and soft separable spaces, and some basic properties of these concepts are explored.
Keywords: soft sets, soft first-countable spaces, soft second countable spaces, soft separable spaces, soft Lindelöf.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2418869 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method
Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei
Abstract:
As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1422868 Comparison of the Existing Methods in Determination of the Characteristic Polynomial
Authors: Mohammad Saleh Tavazoei, Mohammad Haeri
Abstract:
This paper presents comparison among methods of determination of the characteristic polynomial coefficients. First, the resultant systems from the methods are compared based on frequency criteria such as the closed loop bandwidth, gain and phase margins. Then the step responses of the resultant systems are compared on the basis of the transient behavior criteria including overshoot, rise time, settling time and error (via IAE, ITAE, ISE and ITSE integral indices). Also relative stability of the systems is compared together. Finally the best choices in regards to the above diverse criteria are presented.Keywords: Characteristic Polynomial, Transient Response, Filters, Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2016867 Monitoring and Fault-Recovery Capacity with Waveguide Grating-based Optical Switch over WDM/OCDMA-PON
Authors: Yao-Tang Chang, Chuen-Ching Wang, Shu-Han Hu
Abstract:
In order to implement flexibility as well as survivable capacities over passive optical network (PON), a new automatic random fault-recovery mechanism with array-waveguide-grating based (AWG-based) optical switch (OSW) is presented. Firstly, wavelength-division-multiplexing and optical code-division multiple-access (WDM/OCDMA) scheme are configured to meet the various geographical locations requirement between optical network unit (ONU) and optical line terminal (OLT). The AWG-base optical switch is designed and viewed as central star-mesh topology to prohibit/decrease the duplicated redundant elements such as fiber and transceiver as well. Hence, by simple monitoring and routing switch algorithm, random fault-recovery capacity is achieved over bi-directional (up/downstream) WDM/OCDMA scheme. When error of distribution fiber (DF) takes place or bit-error-rate (BER) is higher than 10-9 requirement, the primary/slave AWG-based OSW are adjusted and controlled dynamically to restore the affected ONU groups via the other working DFs immediately.Keywords: Random fault recovery mechanism, Array-waveguide-grating based optical switch (AWG- based OSW), wavelength-division-multiplexing and optical code-divisionmultiple-access (WDM/ OCDMA)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1641866 The Determination of Rating Points of Objects with Qualitative Characteristics and their Usagein Decision Making Problems
Authors: O. Poleshchuk, E. Komarov
Abstract:
The paper presents the method developed to assess rating points of objects with qualitative indexes. The novelty of the method lies in the fact that the authors use linguistic scales that allow to formalize the values of the indexes with the help of fuzzy sets. As a result it is possible to operate correctly with dissimilar indexes on the unified basis and to get stable final results. The obtained rating points are used in decision making based on fuzzy expert opinions.Keywords: complete orthogonal semantic space, qualitativecharacteristic, rating points.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1210865 Application of Generalized Taguchi and Design of Experiment Methodology for Rebar Production at an Integrated Steel Plant
Authors: S. B. V. S. P. Sastry, V. V. S. Kesava Rao
Abstract:
In this paper, x-ray impact of Taguchi method and design of experiment philosophy to project relationship between various factors leading to output yield strength of rebar is studied. In bar mill of an integrated steel plant, there are two production lines called as line 1 and line 2. The metallic properties e.g. yield strength of finished product of the same material is varying for a particular grade material when rolled simultaneously in both the lines. A study has been carried out to set the process parameters at optimal level for obtaining equal value of yield strength simultaneously for both lines.
Keywords: Bar mill, design of experiment, Taguchi, yield strength.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2096864 The Application of the Queuing Theory in the Traffic Flow of Intersection
Authors: Shuguo Yang, Xiaoyan Yang
Abstract:
It is practically significant to research the traffic flow of intersection because the capacity of intersection affects the efficiency of highway network directly. This paper analyzes the traffic conditions of an intersection in certain urban by the methods of queuing theory and statistical experiment, sets up a corresponding mathematical model and compares it with the actual values. The result shows that queuing theory is applied in the study of intersection traffic flow and it can provide references for the other similar designs.
Keywords: Intersection, Queuing theory, Statistical experiment, System metrics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7546863 Investigation of Wave Atom Sub-Bands via Breast Cancer Classification
Authors: Nebi Gedik, Ayten Atasoy
Abstract:
This paper investigates successful sub-bands of wave atom transform via classification of mammograms, when the coefficients of sub-bands are used as features. A computer-aided diagnosis system is constructed by using wave atom transform, support vector machine and k-nearest neighbor classifiers. Two-class classification is studied in detail using two data sets, separately. The successful sub-bands are determined according to the accuracy rates, coefficient numbers, and sensitivity rates.
Keywords: Breast cancer, wave atom transform, SVM, k-NN.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1075862 Existence and Global Exponential Stability of Periodic Solutions of Cellular Neural Networks with Distributed Delays and Impulses on Time Scales
Authors: Daiming Wang
Abstract:
In this paper, by using Mawhin-s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results.
Keywords: Periodic solutions, global exponential stability, coincidence degree, M-matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1465861 Measurement Fractional Order Sallen-Key Filters
Authors: Ahmed Soltan, Ahmed G. Radwan, Ahmed M. Soliman
Abstract:
This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.
Keywords: Analog Filter, Low-Pass Filter, Fractance, Sallen-Key, Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3146860 Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces
Authors: Ismat Beg, Asma Rashid Butt
Abstract:
Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.
Keywords: Fixed point, partially ordered set, metric space, set valued mapping.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2035