Jñānābha‎, Vol. 50 (1) (2020), 65-71

A GENERALIZED SUBCLASS OF ALPHA CONVEX BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER

By

Gurmeet Singh1 ,Gagandeep Singh2 and Gurcharanjit Singh3
1
Department of Mathematics, GSSDOS Khalsa College, Patiala-147001, Punjab, India
Email:meetgur111@gmail.com
2
Department of Mathematics, Khalsa College, Amritsar-143001, Punjab, India
Email:kamboj.gagandeep@yahoo.in
3
Department of Mathematics, Punjabi University, Patiala-147002, Punjab, India
Department of Mathematics, GNDU College, Chungh-143001, Punjab, India
Email:dhillongs82@yahoo.com
(Received : January 22, 2020 ; Revised: May 02, 2020)

Abstract

In this present investigation a subclass of alpha convex bi-univalent functions of complex order in the open unit disc U = {z :| z |< 1}, defined by Salagean operator and quasi- subordination is discussed. The estimates on the initial coefficients |a 2 | and |a 3 | for the functions in this subclass are studied. The results obtained in this paper would generalise those already proved by various authors.

2010 Mathematics Subject Classifications: 30C45.
Keywords and phrases: Bi-univalent functions, Salagean operator, Quasi-subordination, Coefficient estimate, Univalent functions.