Application of Chebyshev polynomials to classes of analytic functions

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 is an element of (1/2, t] de functions f, with f(0) = 0, f'(0) = 1, analytic in the open unit disc U = {z :\z\ < 1) satisfying the condition that [GRAPHICS] where H(z,t) is the generating function of the second kind of Chebyshev polynomials. The Fekete-Szego problem in the class is also solved. (C) 2015 Published by Elsevier Masson SAS on behalf of Academie des sciences.