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Metric Modular Spaces

  • Vyacheslav Chistyakov

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Vyacheslav V. Chistyakov
    Pages 1-17
  3. Vyacheslav V. Chistyakov
    Pages 19-44
  4. Vyacheslav V. Chistyakov
    Pages 45-64
  5. Vyacheslav V. Chistyakov
    Pages 65-78
  6. Vyacheslav V. Chistyakov
    Pages 79-91
  7. Vyacheslav V. Chistyakov
    Pages 93-122
  8. Back Matter
    Pages 123-137

About this book

Introduction

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. 

Keywords

convex modular metric semigroup modular Lipschitzian maps modular convergence modular topology

Authors and affiliations

  • Vyacheslav Chistyakov
    • 1
  1. 1.Nizhny NovgorodRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-25283-4
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-25281-0
  • Online ISBN 978-3-319-25283-4
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site