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

Author

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  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan)

  • 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)

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.

Suggested Citation

  • Hari M. Srivastava & Rogayeh Alavi & Saeid Shams & Rasoul Aghalary & Santosh B. Joshi, 2023. "New Criteria for Starlikness and Convexity of a Certain Family of Integral Operators," Mathematics, MDPI, vol. 11(18), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3919-:d:1240210
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    References listed on IDEAS

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    1. Herb Silverman, 1999. "Convex and starlike criteria," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-5, January.
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