PARTIAL SUMS OF GENERALIZED CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING A GAUSSIAN HYPERGEOMETRIC FUNCTION
The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to its sequences of partial sums by involving the Gaussian hypergeometric function. Relevant connections of the results presented here with various known results are briefly indicated. We also mention results which are associated with certain classical orthogonal polynomials (deduced from some of the main results) exhibiting the usefulness of the results presented in this paper.
Sumas Cuasi-Parciales de Funciones Armónicas Univalentes
espanolEn este trabajo obtenemos algunas condiciones bajo las cuales lassumas cuasi-parciales del operador integral Bernardi generalizado que consiste de funciones armonicas univalentes pertenece a una clase similar. EnglishIn this work, we obtain some conditions under which the quasi partial sums of the generalized Bernardi integral operator consisting of the harmonic univalent functions belongs to a similar class.
The Globalization problem for inner automorphisms and Skolem-Noether theorems
We investigate the circumstances under which an inner automorphism of a ring with local units can be built from “local” information. Specifically, we consider three natural “inner” type properties for an automorphism of a ring with local units. We show that every inner automorphism is locally inner but the converse is false, even if the automorphism is “piecewise” inner. On the other hand, we construct a large class of rings for which every locally inner automorphism is actually inner. Finally we obtain some Skolem-Noether type Theorems for infinite matrix and triangular matrix rings.