POLYNOMIAL BOUNDS FOR BIUNIVALENT FUNCTION ASSOCIATED WITH THE PROBABILITY OF GENERALIZED DISTRIBUTION DEFINED BY GENERALIZED POLYLOGARITMS VIA CHEBSHEV POLYNOMIAL

Abstract

We introduced and investigated new subclasses  and  of  bi-univalent functions defined in the open unit disk, involving the probabilities of generalized distribution and generalized polylogarithms subordinate to Chebyshev polynomials. Furthermore, we determined the estimates on the Taylor-Maclaurin coefficients   and   for the functions in the new subclasses introduced here. Also, we used these estimates to established the relevant connections to classical Fekete-Szeg estimate. Several presume new consequences of the results were also established.