In this paper we obtain upper bounds for the second Hankel determinant H2(2) of the classes bi-starlike and bi-convex functions of order β, which we denote by S∗ σ(β) and Kσ(β), respectively. In particular, the estimates for the second Hankel determinat H2(2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.

Inclusion relations for k−uniformly starlike functions under the Dziok-Srivastava operator are established. These results are also extended to k−uniformly convex functions, close-to-convex, and quasi-convex functions.

Given the hypergeometric function F (a, b; c; z) = ∞ P n=0 (a)n(b)n (c)n(1)n zn, we place conditions on a, b and c to guarante that zpF (a, b; c; z) will be in various subclasses of p-valent starlike and p-valent convex functions. Operators related to the hypergeometric function are also examined.

Srivastava-Attiya operator is used to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk U . For each of these new function classes, several inclusion relationships are established. Some interesting corollaries and applications of the results presented here are also discussed. Mathematics subject classification (2000): 30C45...

"Let $C$ and $S^*$ stand for the classes of convex starlike mapping in $\D$, let $\cc$, $\cs$ denote closures respective hulls. We derive characterizations when convolution mappings $\cc$ is convex, as well starlike. Several terms are given convexity within starlikeness $\cs$. also obtain a correspondence via between $S^*$, correspondences subclasses that have $n$-fold symmetry."

The main object of this paper is to derive the sufficient conditions for the function z {pψq (z)} to be in the class of uniformly starlike and uniformly convex function associated with the parabolic region Re {ω} > |ω − 1| . Further, the hadamard product of the function which are analytic in the open unit disk with negative coefficients are also investigated. Finally, similar results using an i...