# Article ID: MTJPAM-D-20-00023

## Title: On p-Valent Strongly Starlike and Strongly Convex Functions Associated with Generalized Linear Operator

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00023; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 104-111

Document Type: Research Paper

Author(s): Mohamed Kamal Aouf a , Sheza M. El-Deeb b

aDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

bDepartment of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt. Current Address: Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 51452, Saudi Arabia

Received: 11 August 2020, Accepted: 1 December 2020, Published: 25 April 2021.

Corresponding Author: Sheza M. El-Deeb (Email address: shezaeldeeb@yahoo.com)

Full Text: PDF

Abstract

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

Keywords: Analytic functions, p-valent, Strongly starlike, Strongly convex

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