Set Valued Mappings With Applications in Nonlinear Analysis

by O'Regan; Donal

• ISBN13: 9780415284240
• ISBN10: 0415284244
• Edition: 1st
• Format: Hardcover
• Copyright: 2002-09-26
• Publisher: CRC Press

Summary

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

Preface	viii
Positive Lp and Continuous Solutions for Fredholm Integral Inclusions	1	(10)
R.P. Agarwal
M. Meehan
D. O'Regan
A Note on the Structure of the Solution Set for the Cauchy Differential Inclusion in Banach Spaces	11	(6)
R.P. Agarwal
D. O'Regan
Fixed Point Theory for Acyclic Maps between Topological Vector Spaces having Sufficiently many Linear Functionals, and Generalized Contractive Maps with Closed Values between Complete Metric Spaces	17	(10)
R.P. Agarwal
D. O'Regan
Using the Integral Manifolds to Solvability of Boundary Value Problems	27	(12)
J. Andres
On the Semicontinuity of Nonlinear Spectra	39	(10)
J. Appell
G. Conti
P. Santucci
Existence Results for Two-point Boundary Value Problems via Set-valued Analysis	49	(14)
P. Candito
Generalized Strongly Nonlinear Implicit Quasi-variational Inequalities for Fuzzy Mappings	63	(16)
Y.J. Cho
S.H. Shim
N.J. Huang
S.M. Kang
Vector Variational Inequalities, Multi-objective Optimizations, Pareto Optimality and Applications	79	(50)
M.S.R. Chowdhury
E. Tarafdar
Variational Principle and Fixed Points	129	(8)
P.Z. Daffer
H. Kaneko
W. Li
On the Baire Category Method in Existence Problems for Ordinary and Partial Differential Inclusions	137	(12)
F.S. De Blasi
G. Pianigiani
Maximal Element Principles on Generalized Convex Spaces and Their Applications	149	(26)
X.P. Ding
Fixed Point Results for Multivalued Contractions on Gauge Spaces	175	(8)
M. Frigon
The Study of Variational Inequalities and Applications to Generalized Complementarity Problems, Fixed Point Theorems of Set-valued Mappings and Minimization Problems	183	(22)
G. Isac
E. Tarafdar
G.X.-Z. Yuan
Remarks on the Existence of Maximal Elements with Respect to a Binary Relation in Non-compact Topological Spaces	205	(8)
G. Isac
G.X.-Z. Yuan
Periodic Solutions of a Singularly Perturbed System of Differential Inclusions in Banach Spaces	213	(14)
M. Kamenski
P. Nistri
Constrained Differential Inclusions	227	(24)
W. Kryszewski
Nonlinear Boundary Value Problems with Multivalued Terms	251	(36)
N. Matzakos
N.S. Papageorgiou
Optimal Control of a Class of Nonlinear Parabolic Problems with Multivalued Terms	287	(24)
N. Matzakos
N.S. Papageorgiou
N. Yannakakis
Continuation Theory for A-Proper Mappings and their Uniform Limits and Nonlinear Perturbations of Fredholm Mappings	311	(50)
P.S. Milojevic
Existence Theorems for Strongly Accretive Operators in Banach Spaces	361	(8)
C.H. Morales
A Kneser Type Property for the Solution Set of a Semilinear Differential Inclusion with Lower Semicontinuous Nonlinearity	369	(14)
V. Obukhovskii
P. Zecca
A Nonlinear Multivalued Problem with Nonlinear Boundary Conditions	383	(20)
M. Palmucci
F. Papalini
Extensions of Monotone Sets	403	(8)
S. Park
Convergence of Iterates of Nonexpansive Set-valued Mappings	411	(10)
S. Reich
A.J. Zaslavski
A Remark on the Intersection of a Lower Semicontinuous Multifunction and a Fixed Set	421	(4)
B. Ricceri
Random Approximations and Random Fixed Point Theorems for Set-valued Random Maps	425	(6)
N. Shahzad
Existence Theorems for Two-variable Functions and Fixed Point Theorems for Set-valued Mappings	431	(18)
W. Takahashi
An Extension Theorem and Duals of Gale-Mas-Colell's and Shafer-Sonnenschein's Theorems	449	(12)
K.-K. Tan
Z. Wu
Iterative Algorithms for Nonlinear Variational Inequalities Involving Set-valued H-Cocoercive Mappings	461
R.U. Verma