(untitled) (Physical Education, Health and Social Sciences, 2025)
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 |a_2 | and |a_3 |, 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.