Coefficient Bounds for a Subclass of Bi-Univalent Functions Involving the Salagean Differential Operator and Generalized Telephone Numbers

Abstract

This paper investigates a newly defined a specific division of the function set Σ, That comprises  holomorphic and bi-univalent functions in the interior of the unit disk. This subclass is formulated  using the Salagean differential operator and incorporates generalized telephone numbers. Moreover,  we establish bounds for the Taylor-Maclaurin coefficients |a2| and |a3|, highlighting the influence  of generalized telephone numbers in comparison with bi-univalent function subclasses utilizing the  Salagean differential operator in conjunction with the by certain new functions putting in the function  class gives some recent findings. Additionally, we discuss the theoretical computational relevance of  these function classes in modeling complex systems and their potential applications in algorithmic  analysis.