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Metric modular spaces

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Metric modular spaces/ by Vyacheslav V. Chistyakov.
Author:	Chistyakov, Vyacheslav V.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xiii, 137 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Metric spaces. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-25283-4
ISBN:	9783319252834

Metric modular spaces
Chistyakov, Vyacheslav V.

Metric modular spaces[electronic resource] /by Vyacheslav V. Chistyakov. - Cham :Springer International Publishing :2015. - xiii, 137 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

1.Classes of Modulars -- 2. Metrics on Modular Spaces -- 3. Modular Transforms -- 4. Topologies on Modular Spaces -- 5. Bounded and Regulated Mappings -- 6. Mappings of Bounded Generalized Variation -- Appendix -- References.

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.

ISBN: 9783319252834

Standard No.: 10.1007/978-3-319-25283-4doiSubjects--Topical Terms:

527849
Metric spaces.

LC Class. No.: QA611.28

Dewey Class. No.: 514.325

Metric modular spaces
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490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a 1.Classes of Modulars -- 2. Metrics on Modular Spaces -- 3. Modular Transforms -- 4. Topologies on Modular Spaces -- 5. Bounded and Regulated Mappings -- 6. Mappings of Bounded Generalized Variation -- Appendix -- References.
520 $a 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.
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