New Criteria for Starlikness and Convexity of a Certain Family of Integral Operators

Date

2023

Authors

Srivastava, Hari M.
Alavi, Rogayeh
Shams, Saeid
Aghalary, Rasoul
Joshi, Santosh B.

Journal Title

Journal ISSN

Volume Title

Publisher

Mathematics

Abstract

In this paper, we first modify one of the most famous theorems on the principle of differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using this modified form, we generalize and improve several results, which appeared recently in the literature on the geometric function theory of complex analysis. We also prove some simple conditions for starlikeness, convexity, and the strong starlikeness of several one-parameter families of integral operators, including (for example) a certain m-convex integral operator and the familiar Bernardi integral operator.

Description

Keywords

analytic functions, univalent functions, principle of differential subordination, fixed initial Taylor-Maclarin coefficient, integral operators, starlike functions, convex functions, Janowski starlike function class, µ-convex integral operator, Bernardi operator, Schwarz lemma

Citation

Srivastava, H. M., Alavi, R., Shams, S., Aghalary, R., & Joshi, S. B. (2023). New criteria for starlikness and convexity of a certain family of integral operators. Mathematics, 11(18), 3919. https://doi.org/10.3390/math11183919