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

Hari M. Srivastava (), Rogayeh Alavi, Saeid Shams, Rasoul Aghalary and Santosh B. Joshi
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Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Rogayeh Alavi: Department of Mathematics, Faculty of Science, Urmia University, Urmia 57561-51818, Iran
Saeid Shams: Department of Mathematics, Faculty of Science, Urmia University, Urmia 57561-51818, Iran
Rasoul Aghalary: Department of Mathematics, Faculty of Science, Urmia University, Urmia 57561-51818, Iran
Santosh B. Joshi: Department of Mathematics, Walchand College of Engineering, Sangli 416415, Maharashtra, India

Mathematics, 2023, vol. 11, issue 18, 1-20

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 μ -convex integral operator and the familiar Bernardi integral operator.

Keywords: analytic functions; univalent functions; principle of differential subordination; fixed initial Taylor-Maclarin coefficient; integral operators; starlike functions; convex functions; Janowski starlike function class; ?-convex integral operator; Bernardi operator; Schwarz lemma (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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