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

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

doi:10.3390/math11183919

Open AccessArticle

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

by

Hari M. Srivastava

^{1,2,3,4,5,6,*}

,

Rogayeh Alavi

⁷

,

Saeid Shams

⁷

,

Rasoul Aghalary

⁷

and

Santosh B. Joshi

⁸

¹

Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada

²

Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

³

Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

⁴

Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan

⁵

Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 32023, Taiwan

⁶

Section of Mathematics, International Telematic University Uninettuno, 00186 Rome, Italy

⁷

Department of Mathematics, Faculty of Science, Urmia University, Urmia 57561-51818, Iran

⁸

Department of Mathematics, Walchand College of Engineering, Sangli 416415, Maharashtra, India

^*

Author to whom correspondence should be addressed.

Mathematics 2023, 11(18), 3919; https://doi.org/10.3390/math11183919

Submission received: 13 July 2023 / Revised: 6 September 2023 / Accepted: 13 September 2023 / Published: 14 September 2023

(This article belongs to the Special Issue Current Topics in Geometric Function Theory)

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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; μ-convex integral operator; Bernardi operator; Schwarz lemma

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MDPI and ACS Style

Srivastava, H.M.; Alavi, R.; Shams, S.; Aghalary, R.; Joshi, S.B. New Criteria for Starlikness and Convexity of a Certain Family of Integral Operators. Mathematics 2023, 11, 3919. https://doi.org/10.3390/math11183919

AMA Style

Srivastava HM, Alavi R, Shams S, Aghalary R, Joshi SB. New Criteria for Starlikness and Convexity of a Certain Family of Integral Operators. Mathematics. 2023; 11(18):3919. https://doi.org/10.3390/math11183919

Chicago/Turabian Style

Srivastava, Hari M., Rogayeh Alavi, Saeid Shams, Rasoul Aghalary, and Santosh B. Joshi. 2023. "New Criteria for Starlikness and Convexity of a Certain Family of Integral Operators" Mathematics 11, no. 18: 3919. https://doi.org/10.3390/math11183919

APA Style

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

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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