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Fixed Point Theory in Modular Function Spaces (Paperback, Softcover reprint of the original 1st ed. 2015)
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Fixed Point Theory in Modular Function Spaces (Paperback, Softcover reprint of the original 1st ed. 2015)
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This monograph provides a concise introduction to the main results
and methods of the fixed point theory in modular function spaces.
Modular function spaces are natural generalizations of both
function and sequence variants of many important spaces like
Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz,
Calderon-Lozanovskii spaces, and others. In most cases,
particularly in applications to integral operators, approximation
and fixed point results, modular type conditions are much more
natural and can be more easily verified than their metric or norm
counterparts. There are also important results that can be proved
only using the apparatus of modular function spaces. The material
is presented in a systematic and rigorous manner that allows
readers to grasp the key ideas and to gain a working knowledge of
the theory. Despite the fact that the work is largely
self-contained, extensive bibliographic references are included,
and open problems and further development directions are suggested
when applicable. The monograph is targeted mainly at the
mathematical research community but it is also accessible to
graduate students interested in functional analysis and its
applications. It could also serve as a text for an advanced course
in fixed point theory of mappings acting in modular function
spaces.
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