International Journal of Nonlinear Analysis and Applications

A new subclass of Ma-Minda starlike functions associated with a heart-shaped curve

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

In this paper, we extend the q-derivative operator, which plays an essential role in quantum calculus. Indeed, by using the Hadamard product and generalized Koebe function we define the following (α,β,γ)-derivative operator
dα,β,γf(z)=1z{f(z)∗Lα,β,γ(z)},
where
Lα,β,γ(z)=2(1−γ)z(1−αz)(1−βz),
and α∈[−1,1], β∈[−1,1], αβ≠±1 and γ∈[0,1). Then by subordination relation, the operator dα,β,γf(z), and a special function ϕδ(z)=1+δz/exp⁡(δz) (0<δ≤1), we define a new particular Ma-Minda class. We investigate some properties of this class, such as, radius problem and coefficient estimate.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 7
July 2025
Pages 37-46
  • Receive Date: 23 January 2023
  • Revise Date: 02 March 2024
  • Accept Date: 13 July 2024