**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2304

# Search results for: Fixed point theorem

##### 2304 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets

**Authors:**
Menglong Su,
Shaoyun Shi,
Qing Xu

**Abstract:**

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

**Keywords:**
interior path following method,
general Brouwer fixed
point theorem,
non-convex sets,
globally convergent algorithm

##### 2303 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem

**Authors:**
Adil AL-Rammahi

**Abstract:**

In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.

**Keywords:**
Fredholm integral equation,
power series,
Banach fixed point theorem,
Linear Systems.

##### 2302 Constructive Proof of Tychonoff’s Fixed Point Theorem for Sequentially Locally Non-Constant Functions

**Authors:**
Yasuhito Tanaka

**Abstract:**

We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.

**Keywords:**
sequentially locally non-constant functions,
Tychonoff’s
fixed point theorem,
constructive mathematics.

##### 2301 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator

**Authors:**
Lv Yuhua

**Abstract:**

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Cone,
fixed point index,
eigenvalue problem,
p-Laplace operator,
positive solutions.

##### 2300 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem

**Authors:**
Thanin Sitthiwirattham,
Jiraporn Reunsumrit

**Abstract:**

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

**Keywords:**
Positive solution,
Boundary value problem,
Fixed
point theorem,
Cone.

##### 2299 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation

**Authors:**
Fengxia Zheng,
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
Boundary value
problem,
Positive solution,
Existence and uniqueness,
Fixed point
theorem of a sum operator.

##### 2298 Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition

**Abstract:**

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

**Keywords:**
Fractional differential equation,
Integral boundary condition,
Schauder fixed point theorem,
Banach contraction principle.

##### 2297 The Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem

**Authors:**
Chuanyun Gu,
Shouming Zhong

**Abstract:**

In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.

**Keywords:**
Fractional differential equation,
Boundary value problem,
Positive solution,
Existence and uniqueness,
Fixed point theorem of a sum operator

##### 2296 Almost Periodicity in a Harvesting Lotka-Volterra Recurrent Neural Networks with Time-Varying Delays

**Authors:**
Yongzhi Liao

**Abstract:**

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feasibility and effectiveness of the main result.

**Keywords:**
positive almost periodic solution,
Lotka-Volterra,
neural
networks,
Banach fixed point theorem,
harvesting

##### 2295 Positive Solutions for Systems of Nonlinear Third-Order Differential Equations with p-Laplacian

**Authors:**
Li Xiguang

**Abstract:**

**Keywords:**
p-Laplacian,
cone,
fixed point theorem,
positive
solution.

##### 2294 Simulation Tools for Fixed Point DSP Algorithms and Architectures

**Authors:**
K. B. Cullen,
G. C. M. Silvestre,
N. J. Hurley

**Abstract:**

This paper presents software tools that convert the C/Cµ floating point source code for a DSP algorithm into a fixedpoint simulation model that can be used to evaluate the numericalperformance of the algorithm on several different fixed pointplatforms including microprocessors, DSPs and FPGAs. The tools use a novel system for maintaining binary point informationso that the conversion from floating point to fixed point isautomated and the resulting fixed point algorithm achieves maximum possible precision. A configurable architecture is used during the simulation phase so that the algorithm can produce a bit-exact output for several different target devices.

**Keywords:**
DSP devices,
DSP algorithm,
simulation model,
software

##### 2293 Exponential Stability of Periodic Solutions in Inertial Neural Networks with Unbounded Delay

**Authors:**
Yunquan Ke,
Chunfang Miao

**Abstract:**

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

**Keywords:**
Inertial neural networks,
unbounded delay,
fixed-point theorem,
Lyapunov function,
periodic solutions,
exponential stability.

##### 2292 On the Maximum Theorem: A Constructive Analysis

**Authors:**
Yasuhito Tanaka

**Abstract:**

**Keywords:**
Maximum theorem,
Constructive mathematics,
Sequentially
locally at most one maximum.

##### 2291 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions.

##### 2290 On Tarski’s Type Theorems for L-Fuzzy Isotone and L-Fuzzy Relatively Isotone Maps on L-Complete Propelattices

**Authors:**
František Včelař,
Zuzana Pátíková

**Abstract:**

**Keywords:**
Fixed point,
L-complete propelattice,
L-fuzzy
(relatively) isotone map,
residuated lattice,
transitivity.

##### 2289 The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions.

##### 2288 Unique Positive Solution of Nonlinear Fractional Differential Equation Boundary Value Problem

**Authors:**
Fengxia Zheng

**Abstract:**

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

**Keywords:**
Fractional differential equation,
boundary value problem,
positive solution,
existence and uniqueness,
fixed point theorem,
mixed monotone operator.

##### 2287 A Reconfigurable Processing Element for Cholesky Decomposition and Matrix Inversion

**Authors:**
Aki Happonen,
Adrian Burian,
Erwin Hemming

**Abstract:**

**Keywords:**
Cholesky Decomposition,
Fixed-point,
Matrix
inversion,
Reconfigurable processing.

##### 2286 Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation with Integral Boundary Conditions

**Authors:**
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
positive solution,
existence and uniqueness,
fixed point theorem,
generalized concave
and convex operator,
integral boundary conditions.

##### 2285 A Reconfigurable Processing Element Implementation for Matrix Inversion Using Cholesky Decomposition

**Authors:**
Aki Happonen,
Adrian Burian,
Erwin Hemming

**Abstract:**

**Keywords:**
Cholesky Decomposition,
Fixed-point,
Matrixinversion,
Reconfigurable processing.

##### 2284 Common Fixed Point Theorems for Co-Cyclic Weak Contractions in Compact Metric

**Authors:**
Alemayehu Geremew Negash

**Abstract:**

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces.

**Keywords:**
Cyclic weak contraction,
Co-cyclic weak contraction,
Co-cyclic representation,
Common fixed point.

##### 2283 Error Propagation of the Hidden-Point Bar Method: Effect of Bar Geometry

**Authors:**
Said M. Easa,
Ahmed Shaker

**Abstract:**

**Keywords:**
Hidden point,
accuracy,
error propagation,
surveying,
evaluation,
simulation,
geometry.

##### 2282 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.

##### 2281 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular differential
equation.

##### 2280 Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra

**Authors:**
M. Khouil,
N. Saber,
M. Mestari

**Abstract:**

In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision.

**Keywords:**
Collision identification,
fixed time,
convex polyhedra,
neural network,
AMAXNET.

##### 2279 Existence of Solution for Boundary Value Problems of Differential Equations with Delay

**Authors:**
Xiguang Li

**Abstract:**

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

**Keywords:**
Banach space,
boundary value problem,
differential equation,
delay.

##### 2278 Existence of Solution for Singular Two-point Boundary Value Problem of Second-order Differential Equation

**Authors:**
Xiguang Li

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

**Keywords:**
Singular differential equation,
boundary value problem,
coin,
fixed point theory.

##### 2277 IFS on the Multi-Fuzzy Fractal Space

**Authors:**
Nadia M. G. AL-Sa'idi,
Muhammad Rushdan Md. Sd.,
Adil M. Ahmed

**Abstract:**

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

**Keywords:**
Fuzzy metric space,
Fuzzy fractal space,
Multi fuzzy
fractal space.

##### 2276 Positive Solutions of Second-order Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

**Keywords:**
Banach space,
cone,
fixed point index,
singular equation.

##### 2275 Almost Periodic Solution for an Impulsive Neural Networks with Distributed Delays

**Authors:**
Lili Wang

**Abstract:**

By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and effectiveness of the results.

**Keywords:**
Almost periodic solution,
Exponential stability,
Neural networks,
Impulses.