Fixed Point Theory in Ordered Sets and Applications

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Fixed Point Theory in Ordered Sets and Applications / Siegfried Carl, Seppo Heikkilä

資料種別:

電子ブック

出版情報:

SpringerLink Books - AutoHoldings
Springer New York, 2011

著者名:

ISBN:

9781441975843 [1441975845]
9786612973765 [6612973765]
9781489981783 [1489981780]

書誌ID:

OB00493928

子書誌情報

フルテキスト

所蔵情報

書誌詳細

言語:

英語

目次情報:

Preface

Introduction / 1：

Fundamental Order-Theoretic Principles / 2：

Recursions and Iterations in Posets / 2.1：

Fixed Point Results in Posets / 2.2：

Fixed Points for Set-Valued Functions / 2.2.1：

Fixed Points for Single-Valued Functions / 2.2.2：

Comparison and Existence Results / 2.2.3：

Algorithmic Methods / 2.2.4：

Solvability of Operator Equations and Inclusions / 2.3：

Inclusion Problems / 2.3.1：

Single-Valued Problems / 2.3.2：

Special Cases / 2.4：

Fixed Point Results in Ordered Topological Spaces / 2.4.1：

Equations and Inclusions in Ordered Normed Spaces / 2.4.2：

Fixed Point Results for Maximalizing Functions / 2.5：

Preliminaries / 2.5.1：

Main Results / 2.5.2：

Examples and Remarks / 2.5.3：

Notes and Comments / 2.6：

Multi-Valued Variational Inequalities / 3：

Introductory Example / 3.1：

Multi-Valued Elliptic Variational Inequalities / 3.2：

The Sub-Supersolution Method / 3.2.1：

Directedness of Solution Set / 3.2.2：

Extremal Solutions / 3.2.3：

Equivalence to Variational-Hemivariational Inequality / 3.2.4：

Multi-Valued Parabolic Variational Inequalities / 3.3：

Notion of Sub-Supersolution / 3.3.1：

Multi-Valued Parabolic Equation / 3.3.2：

Parabolic Variational Inequality / 3.3.3：

Discontinuous Multi-Valued Elliptic Problems / 3.4：

Nonlocal and Discontinuous Elliptic Inclusions / 4.1：

Hypotheses, Main Result, and Preliminaries / 4.1.1：

Proof of Theorem 4.1 / 4.1.2：

Application: Difference of Clarke's Gradient and Subdifferential / 4.1.3：

State-Dependent Clarke's Gradient Inclusion / 4.2：

Statement of the Problem / 4.2.1：

Notions, Hypotheses, and Preliminaries / 4.2.2：

Existence and Comparison Result / 4.2.3：

Application: Multiplicity Results / 4.2.4：

Discontinuous Elliptic Problems via Fixed Points for Multifunctions / 4.3：

Abstract Fixed Point Theorems for Multi-Functions / 4.3.1：

Discontinuous Elliptic Functional Equations / 4.3.2：

Implicit Discontinuous Elliptic Functional Equations / 4.3.3：

Discontinuous Multi-Valued Evolutionary Problems / 4.4：

Discontinuous Parabolic Inclusions with Clarke's Gradient / 5.1：

Implicit Functional Evolution Equations / 5.2：

Main Result / 5.2.1：

Generalization and Special Cases / 5.2.3：

Application / 5.2.4：

Banach-Valued Ordinary Differential Equations / 5.3：

Cauchy Problems / 6.1：

A Uniqueness Theorem of Nagumo Type / 6.1.1：

Existence Results / 6.1.3：

Existence and Uniqueness Results / 6.1.4：

Dependence on the Initial Value / 6.1.5：

Well-Posedness of a Semilinear Cauchy Problem / 6.1.6：

Nonlocal Semilinear Differential Equations / 6.2：

Existence and Comparison Results / 6.2.1：

Applications to Multipoint Initial Value Problems / 6.2.2：

Higher Order Differential Equations / 6.3：

Well-Posedness Results / 6.3.1：

Semilinear Problem / 6.3.2：

Singular Differential Equations / 6.3.3：

First Order Explicit Initial Value Problems / 6.4.1：

First Order Implicit Initial Value Problems / 6.4.2：

Second Order Initial Value Problems / 6.4.3：

Second Order Boundary Value Problems / 6.4.4：

Functional Differential Equations Containing Bochner Integrable Functions / 6.5：

Hypotheses and Preliminaries / 6.5.1：

Banach-Valued Integral Equations / 6.5.2：

Integral Equations in HL-Spaces / 7.1：

Fredholm Integral Equations / 7.1.1：

Volterra Integral Equations / 7.1.2：

Application to Impulsive IVP / 7.1.3：

A Volterra Equation Containing HL Integrable Functions / 7.1.4：

Urysohn Equations / 7.2：

Evolution Equations / 7.2.3：

Existence and Uniqueness Result / 7.3.1：

Application to a Cauchy Problem / 7.3.3：

Extremal Solutions of Evolution Equations / 7.3.6：

Evolution Equations Containing Bochner Integrable Functions / 7.3.7：

Game Theory / 7.3.8：

Pure Nash Equilibria for Finite Simple Normal-Form Games / 8.1：

An Application to a Pricing Game / 8.1.1：

Pure and Mixed Nash Equilibria for Finite Normal-Form Games / 8.2：

Existence Result for the Greatest Nash Equilibrium / 8.2.1：

Comparison Result for Utilities / 8.2.3：

Dual Results / 8.2.4：

Applications to Finite Supermodular Games / 8.2.5：

Application to a Multiproduct Pricing Game / 8.2.6：

Pure Nash Equilibria for Normal-Form Games / 8.3：

Extreme Value Results / 8.3.1：

Smallest and Greatest Pure Nash Equilibria / 8.3.2：

Applications to a Multiproduct Pricing Game / 8.3.3：

Minimal and Maximal Pure Nash Equilibria / 8.3.5：

Pure and Mixed Nash Equilibria of Normal-Form Games / 8.4：

Definitions and Auxiliary Results / 8.4.1：

Applications to Supermodular Games / 8.4.2：

Undominated and Weakly Dominating Strategies and Weakly Dominating Pure Nash Equilibria for Normal-Form Games / 8.5：

Existence of Undominated Strategies / 8.5.1：

Existence of Weakly Dominating Strategies and Pure Nash Equilibria / 8.5.2：

Examples / 8.5.3：

Pursuit and Evasion Game / 8.6：

Winning Strategy / 8.6.1：

Applications and Special Cases / 8.6.3：

Appendix / 8.7：

Analysis of Vector-Valued Functions / 9.1：

Âµ-Measurability and Âµ-Integrability of Banach-Valued Functions / 9.1.1：

HL Integrability / 9.1.2：

Integrals of Derivatives of Vector-Valued Functions / 9.1.3：

Convergence Theorems for HL Integrable Functions / 9.1.4：

Ordered Normed Spaces of HL Integrable Functions / 9.1.5：

Chains in Ordered Function Spaces / 9.2：

Chains of Locally Bochner Integrable Functions / 9.2.1：

Chains of HL Integrable and Locally HL Integrable Functions / 9.2.3：

Chains of Continuous Functions / 9.2.4：

Chains of Random Variables / 9.2.5：

Properties of Order Intervals and Balls in Ordered Function Spaces / 9.2.6：

Sobolev Spaces / 9.3：

Definition of Sobolev Spaces / 9.3.1：

Chain Rule and Lattice Structure / 9.3.2：

Operators of Monotone Type / 9.4：

Main Theorem on Pseudomonotone Operators / 9.4.1：

Leray-Lions Operators / 9.4.2：

Multi-Valued Pseudomonotone Operators / 9.4.3：

First Order Evolution Equations / 9.5：

Evolution Triple and Generalized Derivative / 9.5.1：

Existence Results for Evolution Equations / 9.5.2：

Calculus of Clarke's Generalized Gradient / 9.6：

List of Symbols

References

Index

Preface

Introduction / 1：

Fundamental Order-Theoretic Principles / 2：

Recursions and Iterations in Posets / 2.1：

Fixed Point Results in Posets / 2.2：

Fixed Points for Set-Valued Functions / 2.2.1：

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