Commenced in January 2007
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Edition: International
Paper Count: 3
Search results for: starlike
3 Some Inequalities Related with Starlike Log-Harmonic Mappings
Authors: Melike Aydoğan, Dürdane Öztürk
Abstract:
Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).Keywords: starlike log-harmonic functions, univalent functions, distortion theorem
Procedia PDF Downloads 4942 Subclass of Close-To-Convex Harmonic Mappings
Authors: Jugal K. Prajapat, Manivannan M.
Abstract:
In this article we have studied a class of sense preserving harmonic mappings in the unit disk D. Let B⁰H (α, β) denote the class of sense-preserving harmonic mappings f=h+g ̅ in the open unit disk D and satisfying the condition |z h״(z)+α (h׳(z)-1) | ≤ β - |z g″(z)+α g′(z)| (α > -1, β > 0). We have proved that B⁰H (α, β) is close-to-convex in D. We also prove that the functions in B⁰H (α, β) are stable harmonic univalent, stable harmonic starlike and stable harmonic convex in D for different values of its parameters. Further, the coefficient estimates, growth results, area theorem, boundary behavior, convolution and convex combination properties of the class B⁰H (α, β) of harmonic mapping are obtained.Keywords: analytic, univalent, starlike, convex and close-to-convex
Procedia PDF Downloads 1351 Some Results on Generalized Janowski Type Functions
Authors: Fuad Al Sarari
Abstract:
The purpose of the present paper is to study subclasses of analytic functions which generalize the classes of Janowski functions introduced by Polatoglu. We study certain convolution conditions. This leads to a study of the sufficient condition and the neighborhood results related to the functions in the class S (T; H; F ): and a study of new subclasses of analytic functions that are defined using notions of the generalized Janowski classes and -symmetrical functions. In the quotient of analytical representations of starlikeness and convexity with respect to symmetric points, certain inherent properties are pointed out.Keywords: convolution conditions, subordination, Janowski functions, starlike functions, convex functions
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