Bi-Starlike Function of Complex Order Involving Mathieu-Type Series Associated with Telephone Numbers

Abstract

For the first time, we attempted to define two new sub-classes of bi-univalent functions in the open unit disc of the complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients of functions in these classes were obtained. Moreover, we also determined the Fekete–Szegö inequalities for function in these and several related corollaries.

Keywords

• analytic functions
• bi-univalent functions
• bi-starlike and bi-convex functions
• coefficient bounds
• Mathieu-type series
• Hadamard (convolution) product