Fekete-Szegö Problem for a New Class of Analytic Functions

which are analytic in the open unit disk U {z : z ∈ C and |z| < 1} and S denote the subclass ofA that are univalent in U. A function f z inA is said to be in class S∗ of starlike functions of order zero in U, if R zf ′ z /f z > 0 for z ∈ U. Let K denote the class of all functions f ∈ A that are convex. Further, f is convex if and only if zf ′ z is star-like. A function f ∈ A is said to be close-to-convex with respect to a fixed star-like function g ∈ S∗ if and only if R zf ′ z /g z > 0 for z ∈ U. Let C denote of all such close-to-convex functions 1 . Fekete and Szegö proved a noticeable result that the estimate