Subclasses of Starlike and Convex Functions Associated with Pascal Distribution Series

Basem Aref Frasin*; Sondekola Rudra Swamy; Abbas Kareem Wanas

doi:10.5666/KMJ.2021.61.1.99

Article

Kyungpook Mathematical Journal 2021; 61(1): 99-110

Published online March 31, 2021

Subclasses of Starlike and Convex Functions Associated with Pascal Distribution Series

Basem Aref Frasin*, Sondekola Rudra Swamy, Abbas Kareem Wanas

Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan
e-mail : bafrasin@yahoo.com

Department of Computer Science and Engineering, RV College of Engineering, Bengaluru - 560 059, Karnataka, India
e-mail : mailtoswamy@rediffmail.com

Department of Mathematics, College of Science, University of Al-Qadisiyah, Iraq
e-mail : abbas.kareem.w@qu.edu.iq

Received: May 20, 2020; Revised: October 7, 2020; Accepted: October 13, 2020

Abstract

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Abstract

In the present paper, we determine new characterisations of the subclasses TS∗C(α,β;γ) and TCC(α,β;γ) of analytic functions associated with Pascal distribution series Φqm(z)=z−∑ n=2∞n+m−2m−1qn−1(1−q)mzn. Further, we give necessary and sufficient conditions for an integral operator related to Pascal distribution series Gqmf(z)=∫0z Φ q m(t)tdt to belong to the above classes. Several corollaries and consequences of the main results are also considered.

Keywords: Analytic functions, Hadamard product, Pascal distribution series.