Coefficient bounds and second Hankel determinant for a subclass of symmetric bi-starlike functions involving Euler polynomials

Abstract

Various operators of fractional calculus, as well as their quantum (or q-) extensions have been used widely and successfully in the study of the Taylor-Maclaurin coefficient estimation problems for many different families of normalized analytic, univalent and bi-univalent functions in Geometric Function Theory of Complex Analysis. On the other hand, Numerous writers have extensively employed orthogonal polynomials in the framework of Geometric Function Theory in Complex analysis. The recent and ongoing studies on this topic is primarily what drives us. In this paper, we solve the Fekete-Szegö problem for the symmetric function classes of analytical and bi-univalent functions involving the Euler polynomials. We also give estimates for the coefficients and an upper bound for the second Hankel determinant.