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Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications

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Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications

Donal O'Regan (Taschenbuch, Englisch)

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Beschreibung

This is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein–Šmulian, Grothendick and Dunford–Pettis. Leray–Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford–Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray–Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi–Pera, and Krasnoselskii fixed point theorems and nonlinear Leray–Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulatedin terms of axiomatic measures of weak noncompactness. The authors continue to present some fixed point theorems in a nonempty closed convex of any Banach algebras or Banach algebras satisfying a sequential condition (P) for the sum and the product of nonlinear weakly sequentially continuous operators, and illustrate the theory by considering functional integral and partial differential equations. The existence of fixed points, nonlinear Leray–Schauder alternatives for different classes of nonlinear (ws)-compact operators (weakly condensing, 1-set weakly contractive, strictly quasi-bounded) defined on an unbounded closed convex subset of a Banach space are also discussed. The authors also examine the existence of nonlinear eigenvalues and eigenvectors, as well as the surjectivity of quasibounded operators. Finally, some approximate fixed point theorems for multivalued mappings defined on Banach spaces. Weak and strong topologies play a role here and bothbounded and unbounded regions are considered. The authors explicate a method developed to indicate how to use approximate fixed point theorems to prove the existence of approximate Nash equilibria for non-cooperative games. Fixed point theory is a powerful and fruitful tool in modern mathematics and may be considered as a core subject in nonlinear analysis. In the last 50 years, fixed point theory has been a flourishing area of research. As such, the monograph begins with an overview of these developments before gravitating towards topics selected to reflect the particular interests of the authors. Weniger zeigen

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Produktinformationen

Technische Daten

Erscheinungsdatum

27.05.2018

Sprache

Englisch

EAN

9783319811628

Herausgeber

Springer International Publishing

Sonderedition

Nein

Autor

Donal O'Regan

Seitenanzahl

194

Auflage

Softcover reprint of the original 1st edition 2016

Einbandart

Taschenbuch

Autorenporträt

Donal O'Regan is Professor in the School of Mathematics, Statistics, and Applied Mathematics at the National University of Ireland, Galway. His research interests include differential equations, nonlinear analysis, and fixed point theory. He is the author of several books, including

Schlagwörter

topological spaces, Banach spaces, convex spaces, operator algbras, eigenvalue problems, singlevalued maps, multivalued maps, integral equations, ordinary differential equations, partial differential equations, game theory, weakly sequentially closed graph, weak noncompactness, Banach algebras

Thema-Inhalt

PBKF - Funktionalanalysis und Abwandlungen PBKJ - Differentialrechnung und -gleichungen

Höhe

235 mm

Breite

15.5 cm

Hersteller: Birkhäuser, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH

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