Initial coefficients for generalized subclasses of bi-univalent functions defined with subordination

Gagandeep Singh, Gurcharanjit Singh, and Gurmeet Singh

Address:
1 Department of Mathematics, Khalsa College, Amritsar, Punjab, India
2 Department of Mathematics, GNDU College, Chungh(Tarn-Taran), Punjab, India
3 Department of Mathematics, GSSDGS Khalsa College, Patiala, Punjab, India

E-mail:
kamboj.gagandeep@yahoo.in
dhillongs82@yahoo.com
meetgur111@gmail.com

Abstract: This paper is concerned with certain generalized subclasses of bi-univalent functions defined with subordination in the open unit disc $E=\left\rbrace z:\mid z \mid <1\right\lbrace $. The bounds for the initial coefficients for the functions in these classes are studied. The earlier known results follow as special cases.

AMSclassification: primary 30C45; secondary 30C50.

Keywords: coefficient estimates, analytic functions, univalent functions, bi-univalent functions, generalized Sãlãgean operator, subordination.

DOI: 10.5817/AM2022-2-105