Abstract
The aim of present investigation is to study a new class of analytic function related with the Sokol-Nunokawa class. We derived relationships of this class with strongly starlike functions and obtained many interesting results.
Highlights
A function λ ∈ A is in class S of univalent function if and only if λ(ω1) λ(ω2) implies ω1 ω2, for all ω1, ω2 ∈ E
Let A be the class of functions λ having the series representation, ∞λ(ω) ω + anωn, (1)Let P denote the class of analytic functions of the form p(z) 1 + p1ω + p2ω2 + · · · such that R(p(ω)) > 0 in E
A function λ ∈ C is in class UCV if, for every circular arc φ ⊂ E with center in E, the arc λ(φ) is convex
Summary
A function λ ∈ A is in class S of univalent function if and only if λ(ω1) λ(ω2) implies ω1 ω2, for all ω1, ω2 ∈ E. Let P denote the class of analytic functions of the form p(z) 1 + p1ω + p2ω2 + · · · such that R(p(ω)) > 0 in E. A function λ ∈ S is in class S∗ if and only if R(ωλ′(ω)/λ(ω)) > 0. In 1991, Goodman [1] introduced the class of uniformly convex function UCV.
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