Abstract

In the present paper, we define a new class of normalized analytic functions based on the $\Phi$-like type. Some inequalities are introduced based on the concept of the subordination in the unit disk. The convexity techniques are used to obtain the main result. Some applications are posed on classes of functions such as starlike functions, convex functions, starlike and convex functions of complex order.

Keywords: Univalent functions; Starlike functions; Convex functions; Differential subordination; Superordination; Unit disk; Starlike and convex functions of complex order; $\Phi$-like functions; Convexity techniques.

MSC: 30C99, 30C45

Pages:  33$-$38     

Volume  64 ,  Issue  1 ,  2012