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This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book’s central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus.

Mathematics. --- Dynamics. --- Ergodic theory. --- Functional analysis. --- Integral equations. --- Operator theory. --- Differential equations. --- Mathematical models. --- Functional Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Integral Equations. --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Operator Theory. --- Nonlinear theories. --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Differential Equations. --- Differentiable dynamical systems. --- Functional analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- 517.91 Differential equations --- Equations, Integral --- Functional equations --- Functional calculus --- Calculus of variations --- Integral equations --- Ergodic transformations --- Continuous groups --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Models, Mathematical --- Simulation methods

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Topology --- Operator theory --- Functional analysis --- analyse (wiskunde) --- functies (wiskunde) --- topologie