Coefficient estimates for the class of quasi q-convex functions

Osman Altintaş,Melike Aydoğan

doi:10.3906/mat-1908-108

Abstract

In this paper we introduce and investigate the class of $ P_{q}(\lambda,\beta, A, B)$, which is called quasi q-starlike and quasi q-convex with respect to the values of the parameter $\lambda$. We give coefficient bounds estimates and the results for the main theorem.

Highlights

Let A denote the class of analytic functions in the open unit disc U = {z ∈ C : |z| < 1} of the form∑ ∞ f (z) = z − anzn, an ≥ 0. n=2We say that the function f (z) is subordinate to g(z) and can be represented as f ≺ g, if there exists a function w(z) such that w(0) = 0, |w(z)| < 1, and f (z) = g(w(z))
If g(z) is univalent the above subordination is equivalent to f (0) = g(0) and f (U ) ⊂ g(U )
Quasi-starlike and quasi-convex functions were studied by Altıntaş

Summary

Introduction

1. Introduction Let A denote the class of analytic functions in the open unit disc U = {z ∈ C : |z| < 1} of the form If g(z) is univalent the above subordination is equivalent to f (0) = g(0) and f (U ) ⊂ g(U ) (see [3]). S∗(α) and C(α) are starlike and convex functions of order α respectively such that For α = 0 , S∗ = S∗(0) and C = C(0) are respectively starlike and convex functions in U (see [3]). Uçar Özkan (see [8]) studied some properties of q -starlike and q -close to convex functions.

Results

Conclusion