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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.

Mathematics. --- Operator Theory. --- Functional Analysis. --- Functional analysis. --- Operator theory. --- Mathématiques --- Analyse fonctionnelle --- Théorie des opérateurs --- Fixed point theory. --- Modular functions. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Functions, Modular --- Fixed point theorems (Topology) --- Elliptic functions --- Group theory --- Number theory --- Nonlinear operators --- Coincidence theory (Mathematics) --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis

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Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying. The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis. Prerequisites for the reader are a robust understanding of calculus and linear algebra.

Electronic books. -- local. --- Logic, Symbolic and mathematical. --- Mathematical analysis. --- Mathematical analysis --- Engineering & Applied Sciences --- Applied Mathematics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- 517.1 Mathematical analysis --- Mathematics. --- Analysis (Mathematics). --- Functions of real variables. --- Real Functions. --- Analysis. --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Real variables

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Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying. The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis. Prerequisites for the reader are a robust understanding of calculus and linear algebra.

Functional analysis --- Differential equations --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- mathematische modellen --- wiskunde

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The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.

Fixed point theory. --- Nonlinear operators. --- Operators, Nonlinear --- Fixed point theorems (Topology) --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Operator theory. --- Mathematical optimization. --- Analysis. --- Functional Analysis. --- Operator Theory. --- Optimization. --- Operator theory --- Nonlinear operators --- Coincidence theory (Mathematics) --- Global analysis (Mathematics). --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- 517.1 Mathematical analysis --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal