In this paper, we introduce some new subclasses of analytic functions related to starlike, convex, close-to-convex and quasi-convex functions defined by using a generalized operator and the differential subordination principle. Inclusion relationships for these subclasses are established. Moreover, we introduce some integral-preserving properties. Key-Words: Starlike function; Convex function; ...

A number of interesting criteria were given by earlier workers for a normalized analytic function to be in the familiar class ∗ of starlike functions. The main object of the present paper is to extend and improve each of these earlier results. An application associated with an integral operator c(c >−1) is also considered.

We solve the problem of finding the largest domain D for which, under given ψ and q, the differential subordination ψ(p(z),zp′(z)) ∈ D ⇒ p(z) ≺ q(z), where D and q( ) are regions bounded by conic sections, is satisfied. The shape of the domain D is described by the shape of q( ). Also, we find the best dominant of the differential subordination p(z)+ (zp′(z)/(βp(z)+γ)) ≺ pk(z), when the functio...

T. N. Shanmugam1 and M. P. Jeyaraman2 1 Department of Mathematics, College of Engineering, Anna University, Chennai 600025, India 2 Department of Mathematics, Easwari Engineering College, Chennai 600089, India Correspondence should be addressed to M. P. Jeyaraman, jeyaraman [email protected] Received 27 July 2009; Accepted 8 October 2009 Recommended by Narendra Kumar Govil We apply the general the...