Inequalities involving a class of analytic functions

Abstract

In the present paper, we define a new classof normalized analytic functions based on the $\mathrm{\Phi }$-like type. Someinequalities are introduced based on the concept of thesubordination in the unit disk. The convexity techniques are used toobtain the main result. Some applications are posed on classes offunctions such as starlike functions, convex functions, starlike andconvex functions of complex order.