Certain subclass of alpha-convex bi-univalent functions defined using $q$-derivative operator

Gagandeep Singh and Gurcharanjit Singh

Address:
Department of Mathematics, Khalsa College, Amritsar, Punjab, India
Department of Mathematics, GNDU College, Chungh(Tarn-Taran), Punjab, India

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

Abstract: The present investigation deals with a new subclass of alpha-convex bi-univalent functions in the unit disc $E=\left\rbrace z\colon \mid z \mid <1\right\lbrace $ defined with $q$-derivative operator. Bounds for the first two coefficients and Fekete-Szegö inequality are established for this class. Many known results follow as consequences of the results derived here.

AMSclassification: primary 30C45; secondary 30C50.

Keywords: analytic functions, bi-univalent functions, alpha-convex functions, coefficient bounds, Fekete-Szegö inequality, q-derivative, subordination.

DOI: 10.5817/AM2025-2-63