A GENERAL SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS

In this present work, we consider a general subclass C*[A, B] of closeto-convexfunctions, which denote by f(z) = z +Sigma(infinity)(n=2)a(n)z(n) in U = {z : |z| < 1} and which satisfy the following condition: vertical bar(zf'(z))'/g0(z) - 1 vertical bar<vertical bar A - B(zf'(z))'/g'(z))vertical bar , (-1 <= B < A <= 1), where g(z) is convex univalent function in U. It gives a sufficient condition forfunctions to belong to the class investigated. Moreover, we derive some propertiesincluding the coefficient bounds as well as distortion theorem. Some radius problemsand relationship with other class are also solved. The results presented here wouldgeneralize many earlier work.