# $p$-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator

Volume 26, Issue 2, pp 137--148
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 $\mathcal{J}_{\mu ,p}$.

### Share and Cite

##### ISRP Style

S. M. El-Deeb, G. Murugusundaramoorthy, A. Alburaikan, $p$-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator, Journal of Mathematics and Computer Science, 26 (2022), no. 2, 137--148

##### AMA Style

El-Deeb S. M., Murugusundaramoorthy G., Alburaikan A., $p$-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator. J Math Comput SCI-JM. (2022); 26(2):137--148

##### Chicago/Turabian Style

El-Deeb, S. M., Murugusundaramoorthy, G., Alburaikan, A.. "$p$-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator." Journal of Mathematics and Computer Science, 26, no. 2 (2022): 137--148

### Keywords

• $p$-Valent
• strongly starlike
• strongly convex
• linear $q$-differential Borel operator

•  05A30
•  30C45
•  11B65
•  47B38

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