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A new class B Σ λ (γ , κ) of bi-starlike λ -pseudo functions related to the second Einstein function is presented in this paper. c 2 and c 3 indicate the initial Taylor coefficients of ϕ ∈ B Σ λ (γ , κ) , and the bounds for | c 2 | and | c 3 | are obtained. Additionally, for ϕ ∈ B Σ λ (γ , κ) , we calculate the Fekete–Szegö functional. [ABSTRACT FROM AUTHOR]

We introduce and examine two new subclass of bi-univalent function Σ , defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to the involution numbers. We find initial estimates of the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in the new subclass introduced here. We also obtain a Fekete–Szegö inequality for the new function class. Several new consequences of our results are pointed out, which are new and not yet discussed in association with involution numbers. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The goal of this article is to contemplate coefficient estimates for a new class of analytic functions f associated with generalized telephone numbers to originate certain initial Taylor coefficient estimates and Fekete–Szegö inequality for f in the new function class. Comparable results have been attained for the function f − 1. Further application of our outcomes to certain functions demarcated by convolution products with certain normalized analytic functions in the open unit disk are specified, and we obtain Fekete–Szegö variations for this new function class defined over Poisson and Borel distribution series. [ABSTRACT FROM AUTHOR]