\(p\)-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator

Volume 26, Issue 2, pp 137--148 http://dx.doi.org/10.22436/jmcs.026.02.04

Publication Date: November 05, 2021 Submission Date: July 30, 2021 Revision Date: September 02, 2021 Accteptance Date: September 17, 2021

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Authors

S. M. El-Deeb - Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt. - Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 51452, Saudi Arabia. G. Murugusundaramoorthy - Department of Mathematics, School of Advanced Sciences, Vellore Institute Technology University, Vellore - 632014, India. A. Alburaikan - Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 51452, Saudi Arabia.

Abstract

In this paper, we define two subclasses \(\mathcal{S}^{\ast }\left( \alpha ,m,\delta ,p,q,\lambda ,\gamma ,\beta \right) \) and \(\mathcal{K}\left( \alpha ,m,\delta ,p,q,\lambda ,\gamma ,\beta \right) \) of strongly starlike and strongly convex functions of order \(\beta \) and type \(\gamma \ \)by using the linear \(q\)-differential Borel operator. We also derive some interesting properties, such as inclusion relationships of these classes and the integral operator \(\mathcal{J}_{\mu ,p}\).

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Keywords

• \(p\)-Valent
• strongly starlike
• strongly convex
• linear \(q\)-differential Borel operator

MSC

•  05A30
•  30C45
•  11B65
•  47B38

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