Yaşar Polatoğlu

Reciprocal classes of p-valently spirallike and p-valently Robertson functions

AbstractFor p-valently spirallike and p-valently Robertson functions in the open unit disk U, reciprocal classes Sp(α,β), and Cp(α,β) are introduced. The object of the present paper is to discuss some interesting properties for functions f(z) belonging to the classes Sp(α,β) and Cp(α,β).n 2010 Mathematics Subject Classificationn Primary 30C45

A coefficient inequality for the class of analytic functions in the unit disc.

The aim of this paper is to give a coefficient inequality for the nclass of analytic functions in the unit disc D = { z | | z | 1 } .

Two-point distortion theorems for certain families of analytic functions in the unit disc.

We give two-point distortion theorems for various subfamilies of nanalytic univalent functions. We also find the necessary and nsufficient condition for these subclasses of analytic functions.

SOME PROPERTIES OF q CLOSE-TO-CONVEX FUNCTIONS

Quantum calculus had been used first time by M.E.H.Ismail, E.Merkes and D.Steyr in the theory of univalent functions [5]. In this present paper we examine the subclass of univalent functions which is defined by quantum calculus.

On the class of harmonic mappings which is related to the class of bounded boundary rotation

The class of bounded radius of rotation is generalization of the convex functions. The concept of functions bounded boundary rotation originated from Loewner (1917). But he did not use the present terminology. It was Paatero (1931, 1933) who systematically developed their properties and made an exhaustive study of the class V k .In the present paper we will investigate the class of harmonic mappings which is related to the class of bounded boundary rotation.

Harmonic mappings related to the m-fold starlike functions

In the present paper we will give some properties of the subclass of harmonic mappings which is related to m-fold starlike functions in the open unit disc D = { z | | z | < 1 } . Throughout this paper we restrict ourselves to the study of sense-preserving harmonic mappings. We also note that an elegant and complete treatment theory of the harmonic mapping is given in Durens monograph (Duren, 1983). The main aim of us to investigate some properties of the new class of us which represented as in the following form, S ? H ( m ) = f = h ( z ) + g ( z ) ? | f ? SH ( m ) , g ( z ) h ( z ) ? b 1 p ( z ) , h ( z ) ? S ? ( m ) , p ( z ) ? P ( m ) , where h ( z ) = z + ? n = 1 ∞ a mn + 1 z mn + 1 , g ( z ) = ? n = 0 ∞ b mn + 1 z mn + 1 , | b 1 | < 1 .

Quasiconformal harmonic mappings related to Janowski alpha-spirallike functions

Let fu2009=u2009h(z)+g(z)¯ be a univalent sense-preserving harmonic mapping of the open unit disc Du2009=u2009{z||z|<1}. If f satisfies the condition |ω(z)|u2009=u2009|g′(z)h′(z)| < k,0 < k < 1 then f is called k-quasiconformal harmonic mapping in D. In the present paper we will give some properties of the class of k-quasiconformal mappings related to Janowski alpha-spirallike functions.

Bounded harmonic mappings related to starlike functions

Let fu2009=u2009h(z)+g(z)¯ be a sense-preserving harmonic mapping in the open unit disc Du2009=u2009{z||z| 12′ then f is called bounded harmonic mapping. The main purpose of this paper is to give some properties of the class of bounded harmonic mapping.

An investigation on a new class of harmonic mappings

In the present paper, we give an extension of the idea which was introduced by Sakaguchi (J. Math. Soc. Jpn. 11:72-75, 1959), and we give some applications of this extended idea for the investigation of the class of harmonic mappings.MSC:30C45, 30C55.

Application of the Subordination Principle to the Harmonic Mappings Convex in One Direction with Shear Construction Method

Any harmonic function in the open unit disc can be written as a sum of an analytic and antianalytic functions , where and are analytic functions in and are called the analytic part and the coanalytic part of respectively. Many important questions in the study of the classes of functions are related to bounds on the modulus of functions (growth) or the modulus of the derivative (distortion). In this paper, we consider both of these questions.