An extension of k-uniformly starlike and convex functions are introduced by making use of an integral operator. Inclusion relations and coefficient bounds for these classes are determined and consequently, some known results are generalized. 2000 Mathematics Subject Classification: Primary 30C45; Secondary 30C50.

A comprehensive class of complex-valued harmonic prestarlike univalent functions is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Distortion bounds and extreme points are also obtained. 2000 Mathematics Subject Classification:Primary 30C45, 30C50.

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...

The purpose of the present paper is to derive the Fekete-Szegö inequality for the class , ( ) s M    of normalized analytic functions ( ) f z defined on the open unit disk for which , , ( ( )) ' ( ) s s z f z f z       lies in a region starlike with respect to 1 and symmetric with respect to the real axis.

This article is concerned with the number B D (x) of integer points with relative prime coordinates in p x D, where x is a large real variable and D is a starlike set in the Euclidean plane. Assuming the truth of the Riemann Hypothesis, we establish an asymptotic formula for B D (x). Applications to certain special geometric and arithmetic problems are discussed .