Generalized uniformly close-to-convex functions of order γ and type β

In this paper, a class of analytic functions f defined on the open unit disc satisfying Re{z(D(lambda)(n,alpha)f(z))'/D(lambda)(n,alpha)g(z)} > beta vertical bar z(D(lambda)(n,alpha)f(z))'/D(lambda)(n,alpha)g(z) - 1 vertical bar + gamma, is studied, where beta >= 0, -1 <= gamma < 1, beta + gamma >= 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.