In this paper, a subclass N(λ, α, A, B) of analytic functions is introduced, which is a generalized class of non-Bazilevič functions. The subordination relations, inclusion relations, distortion theorems and inequality properties are discussed by applying differential subordination method.

For analytic functions f (z) in the open unit disk E and convex functions g(z) in E, has proved one theorem which is a generalization of the result by K. Sakaguchi [K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959) 72–75]. The object of the present paper is to generalize the theorem due to Pommerenke.

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; ...

in present paper acertain convolution operator of analytic functions is defined.moreover, subordination- and superordination- preserving propertiesfor a class of analytic operators defined on the space of normalizedanalytic functions in the open unit disk is obtained. we also applythis to obtain sandwich results and generalizations of some knownresults.

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.

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...