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In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space.

Monotone operators. --- Monotonic functions. --- Banach spaces. --- Opérateurs monotones --- Fonctions monotones --- Banach, Espaces de --- Monotone operators --- Monotonic functions --- Banach spaces --- Duality theory (Mathematics) --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Maxima and minima. --- Opérateurs monotones --- EPUB-LIV-FT SPRINGER-B --- Functions, Monotonic --- Minima --- Mathematics. --- Functional analysis. --- Operator theory. --- Calculus of variations. --- Functional Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Operator Theory. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Functions of real variables --- Operator theory --- Algebra --- Mathematical analysis --- Topology --- Functions of complex variables --- Generalized spaces --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis

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Devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure, this book focuses on gradient flows in metric spaces. It covers gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance.

Differential geometry. Global analysis --- Mathematical physics --- Operational research. Game theory --- differentiaalvergelijkingen --- kansrekening --- differentiaal geometrie --- stochastische analyse --- Measure theory --- Metric spaces --- Differential equations, Partial --- Monotone operators --- Evolution equations, Nonlinear --- Mesure, Théorie de la --- Espaces métriques --- Equations aux dérivées partielles --- Opérateurs monotones --- Equations d'évolution non linéaires --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Global analysis (Mathematics). --- Mathematics. --- Global differential geometry. --- Distribution (Probability theory. --- Analysis. --- Measure and Integration. --- Differential Geometry. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Geometry, Differential --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Measure theory. --- Differential geometry. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential geometry --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- 517.1 Mathematical analysis --- Mathematical analysis --- Metric spaces. --- Differential equations, Parabolic. --- Monotone operators. --- Evolution equations, Nonlinear. --- Operator theory --- Parabolic differential equations --- Parabolic partial differential equations --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Nonlinear equations of evolution --- Nonlinear evolution equations --- Differential equations, Nonlinear