Application of Chebyshev polynomials to classes of analytic functions

Abstract

Our objective in this paper is to consider some basic properties of the familiar Chebyshev polynomials in the theory of analytic functions. We investigate some basic useful characteristics for a class H(t), t∈(1/2,1], of functions f, with f(0)=0, f′(0)=1, analytic in the open unit disc U={z:|z|<1} satisfying the condition that1+zf″(z)f′(z)≺H(z,t)=11−2tz+z2(z∈U), where H(z,t) is the generating function of the second kind of Chebyshev polynomials. The Fekete–Szegö problem in the class is also solved.