In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya–Szegö symmetrization principle for functions on R. Several applications of this new inequality are derived. In particular, a sharp affine logarithmic Sobolev inequality is established which is stronger than its classical Euclidean counterpart.

In this paper we obtain the Fekete-Szegö inequality for a class of analytic functions f(z) defined in the open unit disk for which

An anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang's result to any norm from Euclidean norm, and the geometric analogue of this inequality is given. In addition, it implies that the (anisotropic) Pólya-Szegö principle is shown.

In the present paper, we consider a generalised subclass of analytic functions involving arithmetic, geometric and harmonic means. For this function class we obtain an inclusion result, Fekete-Szegö inequality and coefficient bounds for bi-univalent functions.

– We give an alternative proof of a theorem by Brothers and Ziemer concerning extremal functions in the Pólya–Szegö rearrangements inequality for Dirichlet type integrals.  2003 Éditions scientifiques et médicales Elsevier SAS

We prove two new reverse Cauchy–Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C *-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy–Schwarz inequality due to G. Pólya and G. Szegö.

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.