Distortion Theorems In Relation To Linear Integral Operators
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Distortion Theorems in Relation to Linear Integral Operators
Author: Y. Komatu
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The present monograph consists of two parts. Before Part I, a chapter of introduction is supplemented, where an overview of the whole volume is given for reader's convenience. The former part is devoted mainly to expose linear inte gral operators introduced by the author. Several properties of the operators are established, and specializations as well as generalizations are attempted variously in order to make use them in the latter part. As compared with the former part, the latter part is de voted mainly to develop several kinds of distortions under actions of integral operators for various familiar function also absolute modulus. real part. range. length and area. an gular derivative, etc. Besides them, distortions on the class of univalent functions and its subclasses, Caratheodory class as well as distortions by a differential operator are dealt with. Related differential operators play also active roles. Many illustrative examples will be inserted in order to help understanding of the general statements. The basic materials in this monograph are taken from a series of researches performed by the author himself chiefly in the past two decades. While the themes of the papers pub lished hitherto are necessarily not arranged chronologically Preface viii and systematically, the author makes here an effort to ar range them as ,orderly as possible. In attaching the import ance of the self-containedness to the book, some of unfamil iar subjects will also be inserted and, moreover, be wholly accompanied by their respective proofs, though unrelated they may be.
Integration on Infinite-Dimensional Surfaces and Its Applications
Author: A. Uglanov
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-06-29
It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century. At least the author is not aware of any publication concerning this theme, although as early as 1967 L. Gross mentioned that the analysis on infinite dimensional manifolds is a field of research with rather rich opportunities in his classical work [2. This prediction was brilliantly confirmed afterwards, but we shall return to this later on. In those days the integration theory in infinite dimensional linear spaces was essentially developed in the heuristic works of RP. Feynman [1], I. M. Gelfand, A. M. Yaglom [1]). The articles of J. Eells [1], J. Eells and K. D. Elworthy [1], H. -H. Kuo [1], V. Goodman [1], where the contraction of a Gaussian measure on a hypersurface, in particular, was built and the divergence theorem (the Gauss-Ostrogradskii formula) was proved, appeared only in the beginning of the 70s. In this case a Gaussian specificity was essential and it was even pointed out in a later monograph of H. -H. Kuo [3] that the surface measure for the non-Gaussian case construction problem is not simple and has not yet been solved. A. V. Skorokhod [1] and the author [6,10] offered different approaches to such a construction. Some other approaches were offered later by Yu. L. Daletskii and B. D. Maryanin [1], O. G. Smolyanov [6], N. V.
Fixed Point Theory and Best Approximation: The KKM-map Principle
Author: S.P. Singh
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-17
The aim of this volume is to make available to a large audience recent material in nonlinear functional analysis that has not been covered in book format before. Here, several topics of current and growing interest are systematically presented, such as fixed point theory, best approximation, the KKM-map principle, and results related to optimization theory, variational inequalities and complementarity problems. Illustrations of suitable applications are given, the links between results in various fields of research are highlighted, and an up-to-date bibliography is included to assist readers in further studies. Audience: This book will be of interest to graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations and expansions, convex sets and related geometric topics and game theory.