Bi-Univalent Functions Based on Binomial Series-Type Convolution Operator Related with Telephone Numbers

Abstract

This paper introduces two novel subclasses of the function class Σ for bi-univalent functions, leveraging generalized telephone numbers and Binomial series through convolution. The exploration is conducted within the domain of the open unit disk. We delve into the analysis of initial Taylor-Maclaurin coefficients |a2| and |a3|, deriving insights and findings for functions belonging to these new subclasses. Additionally, Fekete-Szegö inequalities are established for these functions. Furthermore, the study unveils a range of new subclasses of Σ, some of which are special cases, yet have not been previously explored in conjunction with telephone numbers. These subclasses emerge as a result of hybrid-type convolution operators. Concluding from our results, we present several corollaries, which stand as fresh contributions in the domain of involution numbers involving hybrid-type convolution operators.

Keywords

• univalent functions
• analytic functions
• bi-univalent functions
• binomial series
• convolution operator
• involution numbers