Generalized uniformly close-to-convex functions of order ? and type ?

Abstract

In this paper, a class of analytic functions f defined on the open unit disc satisfying Re z(Dn,??f(z))0Dn,??g(z)> ?z(Dn,??f(z))0Dn,??g(z)- 1+ ?, is studied, where ? >= 0, -1 = 0. and g is a certain analytic function associated with conic domains. Among other results, inclusion relations and the coefficients bound are studied. Various known special cases of these results are pointed out. A subclass of uniformly quasi-convex functions is also studied.