by using generalized salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.

Abstract In this paper we study two functions F⁢(x) {F(x)} and xmlns:m="http://www.w3.org/1998/Math/MathML">J⁢<m:mo {J(x)} , originally found by Herglotz in 192...

We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation sol...

These notes accompany lectures presented at the Clay Mathematics Institute 2006 Summer School on Arithmetic Geometry. The lectures summarize some recent progress on existence of rational points of projective varieties defined over a function field over an algebraically closed field.