Bohr Radius Problems for Some Classes of Analytic Functions Using Quantum Calculus Approach

Om Ahuja,Naveen Kumar Jain,Swati Anand

doi:10.3390/math8040623

Om Ahuja, Naveen Kumar Jain + Show 1 more

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https://doi.org/10.3390/math8040623

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Abstract

The main purpose of this investigation is to use quantum calculus approach and obtain the Bohr radius for the class of q-starlike (q-convex) functions of order α . The Bohr radius is also determined for a generalized class of q-Janowski starlike and q-Janowski convex functions with negative coefficients.

Highlights

Let D := {z :∈ C : |z| < 1} be the open unit disc in C
Suppose A denote the class of analytic functions in D normalized by f (0) = 0 = f 0 (0) − 1
Let S be the subclass of A consisting of univalent functions in D

Summary

Introduction

Let D := {z :∈ C : |z| < 1} be the open unit disc in C. Suppose A denote the class of analytic functions in D normalized by f (0) = 0 = f 0 (0) − 1. Suppose H(D, Ω) is the class of analytic functions mapping open unit disc D into a domain n. The number 1/3 is commonly called the "Bohr radius" for the class of analytic self-maps f n in D, while the inequality ∑∞. Bohr inequality and their proofs were given in [2,3,4]. The Bohr radius for a class M consisting of analytic functions f of the form f (z) =.

It is a routine to check that

Thus min Re