Coefficient Bounds for Subclasses of Bi Univalent Functions and Their Applications

Abstract

In recent years, assorted fascinating properties and characteristics of the many differentsubclasses of analytic univalent functions are consistently investigated. In this work theclass |-fUSs (_; _; _; _; t) [_ _ _ _ 0, 0 _ _ _ 1, _; | _ 0, and#1048576;1 _ jtj _ and#1048576;1, t 61, newline0 _ _ lt 1] of analytic functions with negative coefficients is introduced in the open newlineunit disk U, janj is estimated. Neighborhood properties, partial sums are obtained. newlineIn the other direction the Taylor-Maclaurin series of the coefficients function newlinesatisfies the general subclasses of C_(_; _; t), G_(_; _; t) and L_(_; _; t). The Faber newlinepolynomial expansion has been applied for the function h(z) belongs to C_(_; _; t), newlineG_(_; _; t)and L_(_; _; t). The values of ja2j and ja3j are ensured in the present newlineresearch.This work also consists of the general subclasses of B_(_; l; t), C_(_; l; t) and D_(_; l; t) of bi-univalent Sakaguchi kind of functions, which are expressed in newlineChebyshev polynomials.This Chebyshev polynomials the Ist and IInd kind are exerted newlineto expose the estimation of ja2j and ja3j. Fekete-Szeg¨o form of inequalities for the newlinefunction in these classes have been obtained. Finally as an application of the functions11+z ; 5z+5 and 2z+2 are considered as a transfer function and Chebyshev typeI]low-passfilter is designed to analyse magnitude and phase response. newlineAdditionally the subclasses B(_; ; t), C(; t), P(_; _; t) and Q(; t) are defined in newlinehypergeometric functions. Sufficient condition for[Gaussian] hypergeometric function newlineto be in the subclass of Sakaguchi kind of order _ is obtained. Necessary and Sufficient conditions are provided with additional restrictions. Moreover integral operator related to the hypergeometric function in the open unit disk U is discussed newline