EAN: 9783319252810

SPRINGERBRIEFS IN MATHEMATICS METRIC MODULAR ...

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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