Integral transforms of functions to be in certain class defined by the combination of starlike and convex functions

Let P-gamma (beta). beta < 1, denote the class of all normalized analytic functions f in the unit disc D = {z epsilon C : |z| < 1} such that Re (e(i phi) ((1 - gamma)f(z)/z + gamma f' (Z) - beta)) > 0, z epsilon D for some phi epsilon R. Let M (mu,alpha), 0 <= mu < 1, denote the pascu class of alpha-convex functions of order mu and given by the analytic condition Re alpha z(zf'(z))' + (1-alpha)zf'(z)/alpha zf'(z) + (1-alpha)f(z) > mu which unifies S*(mu) and C(mu), respectively, the classes of analytic functions that map D onto the starlike and convex domain. In this work, we consider integral transforms of the form V-lambda(f)(z) = integral(1)(0) lambda(t) f(tz)/t dt. The aim of this paper is to find conditions on lambda(t) so that the above transformation carry P-gamma (beta) into M (mu, alpha). As applications, for specific values of lambda(t), it is found that several known integral operators carry P-gamma (beta) into M(mu, alpha). (C) 2012 Elsevier Ltd. All rights reserved.