FEKETE-SZEGÖ INEQUALITY AND ZALCMAN FUNCTIONAL FOR CERTAIN SUBCLASS OF ALPHA-CONVEX FUNCTIONS
By
Gagandeep Singh1 and Gurcharanjit Singh2
1Department of Mathematics, Khalsa College, Amritsar, Punjab, India-143001
2Department of Mathematics, GNDU College, Chungh (TT), Punjab, India-143304
Email: kamboj.gagandeep@yahoo.in,dhillongs82@yahoo.com
(Received: June 28, 2022; In format: July 17, 2022; Finally revised: January 06, 2023; Accepted: January 31, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53102
Abstract
In the present investigation, we introduce a subclass of α-convex functions defined with subordination and associated with Cardioid domain in the open unit disc E = {z ∈ C : |z| < 1}. We establish the bounds for |a2|, |a3| and |a4|, Fekete-SzegÖ inequality and bound for the Zalcman functional for
this class. The results proved earlier will follow as special cases.
2020 Mathematical Sciences Classification: 30C45, 30C50.
Keywords and Phrases: Analytic functions, Alpha-convex functions, Subordination, Cardioid domain, Coefficient bounds, Fekete-SzegÖ inequality, Zalcman functional.
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