COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF CLOSE-TO-CONVEX AND QUASI-CONVEX FUNCTIONS WITH FIXED POINT


By

Gagandeep Singh1 and Gurcharanjit Singh2

1Department of Mathematics, Khalsa College, Amritsar-143001, Punjab, India

2Department of Mathematics, GNDU College, Chungh (TT)-143304, Punjab, India

Email:kamboj.gagandeep@yahoo.in, dhillongs82@yahoo.com

(Received : January 18, 2022; Revised : January 23, 2022 ; Accepted : April 19, 2022)


Abstract

In this paper, we apply the concept of subordination to introduce certain subclasses of close-to-convex and quasiconvex functions with fixed point in the unit disc E = {z :| z |< 1}. We establish the upper bounds of the first four coefficients for these classes. This work will motivate the other researchers of this field to study some more relevant classes.


2020 Mathematical Sciences Classification: 30C45, 30C50.

Keywords and Phrases: Univalent functions, close-to-convex functions, quasi-convex functions, subordination, coeffcient bounds.



[Download full paper]