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.
Number of pages: 245
Weight: 549 g
Dimensions: 235 x 155 x 16 mm
Edition: 2015 ed.
"The book is essentially self-contained and it provides an outstanding resource for those interested in this line of research." (Maria Angeles Japon Pineda, Mathematical Reviews, March, 2016)
"The book is devoted to a comprehensive treatment of what is currently known about the fixed point theory in modular function spaces. ... the book will be useful for all mathematicians whose interests lie in nonlinear analysis, in particular, in the theory of function spaces and fixed point theory." (Peter P. Zabreiko, zbMATH 1318.47002, 2015)