Overview
- Presents an easy and unified way to generate different metrics
- Contains new existence results in nonlinear functional analysis
- Includes important applications to set-valued analysis?
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (6 chapters)
Keywords
About this book
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existence of solutions to ordinary differential equations in Banach spaces with rapidly varying right-hand sides.
Reviews
“This book is a contribution to the general theory of modulars defined on arbitrary sets. … The content of the book is well organized, and the exposition is as self-contained as possible. … this is an interesting book on function spaces theory. It contains a wealth of materials concerning modular spaces and some of their applications. This work should be useful to undergraduate students and certainly to a more general audience of mathematicians and physicists.” (Mohammed Morsli, Mathematical Reviews, September, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Metric Modular Spaces
Authors: Vyacheslav Chistyakov
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-25283-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-25281-0Published: 21 December 2015
eBook ISBN: 978-3-319-25283-4Published: 14 December 2015
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XIII, 137
Number of Illustrations: 2 illustrations in colour
Topics: Several Complex Variables and Analytic Spaces, Ordinary Differential Equations, Functional Analysis, Special Functions