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SpringerBriefs in Mathematics

Metric Modular Spaces

Authors: Chistyakov, Vyacheslav V

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  • 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​
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eBook £34.99
price for United Kingdom (gross)
  • ISBN 978-3-319-25283-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £43.99
price for United Kingdom (gross)
  • ISBN 978-3-319-25281-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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

“Based extensively on the original results of the author, the book generalizes and presents in a unitary way a lot of results on classical modular spaces with applications to the study of function spaces and of nonlinear operators acting on them. It can be recommended to researchers in applied functional analysis, ordinary differential equations and partial differential equations.” (Stefan Cobzaş, zbMATH 1354.46001, 2017)

“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)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook £34.99
price for United Kingdom (gross)
  • ISBN 978-3-319-25283-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £43.99
price for United Kingdom (gross)
  • ISBN 978-3-319-25281-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Metric Modular Spaces
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-25283-4
DOI
10.1007/978-3-319-25283-4
Softcover ISBN
978-3-319-25281-0
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XIII, 137
Number of Illustrations
2 illustrations in colour
Topics