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.

The logarithmic coefficients play an important role for different estimates in the theory of univalent functions.Due to significance recent studies about coefficients, problem obtaining sharp bounds second Hankel determinant these that is $H_{2,1}(F_f/2)$ was paid attention. We recall if $f$ and $F$ are two analytic functions $\mathbb{D}$, function subordinate $F$, written $f(z)\prec F(z)$, the...

In this paper we introduce new subclasses of k-uniformly convex and starlike functions with respect to other points. We provide necessary and sufficient conditions, coefficient estimates, distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for these classes. We also obtain integral means inequalities with the extremal functions for these classes.

In this article, by making use of a q-analogue the familiar Borel distribution, we introduce two new subclasses: S?,?,q symmetric(b, A, B) and conjugate(b,A, starlike convex functions in open unit disk ? with respect to symmetric conjugate points. We obtain some properties including Taylor-Maclaurin coefficient estimates for each these subclasses deduce various corollaries consequences main res...