Set Valued Mappings with Applications in Nonlinear Analysis: 1st Edition (Hardback) book cover

Set Valued Mappings with Applications in Nonlinear Analysis

1st Edition

By Donal O'Regan, Ravi P. Agarwal

CRC Press

480 pages

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Hardback: 9780415284240
pub: 2002-09-26
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Description

Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.

Table of Contents

Positive L^TP and Continuous Solutions for Fredholm Integral Inclusions. A Note on the Structure of the Solution Set for the Cauchy Differential Inclusion in Banach Spaces. Fixed Point Theory for Acylic Maps between Topological Vector Spaces having Sufficiently many Linear Functionals, and Generalized Contractive Maps with Closed Values between Complete Metric Spaces. Using the Integral Manifolds to Solvability of Boundary Value Problems. On the Semicontinuity of Nonlinear Spectra. Existence Results for Two-Point Boundary Value Problems. Generalized Strongly Nonlinear Implicit Quasi-Variational Inequalities for Fuzzy Mappings. Vector Variational Inequalities, Multi-Objective Optimizations, Pareto Optimality and Applications. Variational Principle and Fixed Points. On the Baire Category Method in Existence Problems for Ordinary and Partial Differential Inclusions. Maximal Element Principles on Generalized Convex Spaces and their Applications. Fixed Point Results for Multi-valued Contractions on Gauge Spaces. The Study of Variational Inequalities and Applications to Generalized Complementarity Problems, Fixed Point Theorems of Set-Valued Mappings and Minimization Problems. Remarks on the Existence of Maximal Elements with Respect to a Binary Relation in Non-Compact Topological Spaces. Periodic Solutions of a Singularly Perturbed System of Differential Inclusions in Banach Space. Constrained Differential Inclusions. Nonlinear Boundary Value Problems with Multi-valued Terms. Optimal Control of a Class of Nonlinear Parabolic Problems with Multi-valued Terms. Continuation Theory for A-Proper Mappings and their Uniform Limits and Nonlinear Perturbations of Fredholm Mappings. Existence Theorems for Strongly Accretive Operators in Banch Spaces. A Kneser Type Property for the Solution Set of a Semilinear Differential Inclusion with Lower Semicontinuous Nonlinearity. A Nonlinear Multi-valued Problem with Nonlinear Boundary Conditions. Extensions of Monotone Sets. Convergence of Iterates of Nonexpansive Set-Valued Mappings. A Remark on the Intersection of a Lower Semicontinuous Multi-function and Fixed Set. Random Approximations and Random Fixed Point Theorems for Set-Valued Random Maps.Existence Theorems for Two-Variable Functions and Fixed Point Theorems for Set-Valued Mappings. An Extension Theorem and Duals of Gale-Mas-Colell's and Shafer-Sonnenschein's Theorems. Iterative Algorithms for Nonlinear Variational Inequalities Involving Set-Valued H-Cocoercive Mappings.

About the Series

Mathematical Analysis and Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
MAT037000
MATHEMATICS / Functional Analysis