On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class \(R^{\lambda}(a,c,A,B)\) of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass \(\widetilde {R}^{\lambda}(a,c, A,B)\) of \(R^{\lambda}(a,c,A,B)\) and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.