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Differential Subordination and Differential Superordination for Classes of Admissible Multivalent Functions Associated with a Linear Operator

Author

Listed:
  • Ekram E. Ali

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
    Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said 42521, Egypt)

  • Hari M. Srivastava

    (Department of Mathematics and Staristics, 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)

  • Rabha M. El-Ashwah

    (Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt)

  • Abeer M. Albalahi

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia)

Abstract

In this paper, we first introduce a linear integral operator ℑ p ( a , c , μ ) ( μ > 0 ; a , c ∈ R ; c > a > − μ p ; p ∈ N + : = { 1 , 2 , 3 , … } ) , which is somewhat related to a rather specialized form of the Riemann–Liouville fractional integral operator and its varied form known as the Erdélyi–Kober fractional integral operator. We then derive some differential subordination and differential superordination results for analytic and multivalent functions in the open unit disk U , which are associated with the above-mentioned linear integral operator ℑ p ( a , c , μ ) . The results presented here are obtained by investigating appropriate classes of admissible functions. We also obtain some Sandwich-type results.

Suggested Citation

  • Ekram E. Ali & Hari M. Srivastava & Rabha M. El-Ashwah & Abeer M. Albalahi, 2022. "Differential Subordination and Differential Superordination for Classes of Admissible Multivalent Functions Associated with a Linear Operator," Mathematics, MDPI, vol. 10(24), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4690-:d:999783
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