Generalized Leray-Schauder principles for condensing admissible multifunctions
type: Item
instance of: scholarly article
title: Generalized Leray-Schauder principles for condensing admissible multifunctions
zbMATH Open document ID: 0941.47050
DOI: 10.1007/BF01782607
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2000-01-04T00:00:00Z
review text: Building on a previous paper [Topol. Meth. Nonlinear Anal. 5, 271-277 (1995; Zbl 0862.47035)], the author gives a detailed survey on general fixed point principles of Leray-Schauder type for compact or condensing multifunctions in so-called admissible classes. Among others, these classes contain Kakutani maps, acyclic maps, approachable maps, O'Neill maps, and Górniewicz maps. The methods are purely analytic and do not require topological degree or index theory.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 1383201
zbMATH Keywords: fixed point principles of Leray-Schauder type
zbMATH Keywords: compact or condensing multifunctions
zbMATH Keywords: admissible classes
zbMATH Keywords: Kakutani maps
zbMATH Keywords: acyclic maps
zbMATH Keywords: approachable maps
zbMATH Keywords: O'Neill maps
zbMATH Keywords: Górniewicz maps
author: Sehie Park
reviewed by: Jürgen Appell
MaRDI profile type: Publication
cites work: Q3229089
cites work: Q4308671
cites work: Q3483892
cites work: Approachability and fixed points for non-convex set-valued maps
cites work: Q5533818
cites work: Q5591060
cites work: Punti uniti in trasformazioni a codominio non compatto
cites work: Fixed points of weakly inward multis
cites work: Q3721418
cites work: Fixed Point Theorems for Multi-Valued Transformations
cites work: Q3833104
cites work: Fixed point theorems for multivalued noncompact acyclic mappings
cites work: Fixed Point Theorems and the Fixed Point Index for Multivalued Mappings in Cones
cites work: Eigenvectors for nonlinear maps
cites work: Q4062375
cites work: Q5594100
cites work: Fixed point theorems for contraction mappings with applications to nonexpansive and pseudo-contractive mappings
cites work: A fixed point theorem for k-set-contractions defined in a cone
cites work: Q4087979
cites work: Q3816704
cites work: Q3262490
cites work: Q4118379
cites work: On the Leray-Schauder alternative
cites work: Fixpunktsätze für mengenwertige Abbildungen in lokalkonvexen Räumen
cites work: Fixed point theorems for set-valued maps in infinite dimensional spaces
cites work: Fixed Point Theorems for Condensing Multifunctions
cites work: A Topological Transversality Theorem For Multi-Valued Maps In Locally Convex Spaces With Applications To Neutral Equations
cites work: Quasi-compact non-linear operators in Banach space and applications
cites work: Q5817709
cites work: On the use of KKM multifunctions in fixed point theory and related topics
cites work: Q3976087
cites work: Q5566053
cites work: Approximation Theorems and Fixed Point Theorem in Cones
cites work: Q5612322
cites work: Q4051169
cites work: Q4073972
cites work: Eigenvectors and surjectivity for \(\alpha\)-Lipschitz mappings in Banach spaces
cites work: The fixed point index for local condensing maps
cites work: Q3211862
cites work: Q3993736
cites work: Q4280631
cites work: Q4298697
cites work: Q4877746
cites work: SURFACES OF GENERAL TYPE WITH pg= 1 AND q = 0
cites work: Generalized Leray-Schauder principles for compact admissible multifunctions
cites work: Geometric Properties, Minimax Inequalities, and Fixed Point Theorems on Convex Spaces
cites work: Some Fixed Point Theorems for Composites of Acyclic Maps
cites work: Remarks on Fixed Point Theorems and Their Extensions
cites work: Structure of the fixed points sets of k-set-contractions
cites work: A Degree Theory, Fixed Point Theorems, and Mapping Theorems for Multivalued Noncompact Mappings
cites work: Fixed-point theorems for multivalued noncompact inward maps
cites work: An Elementary Version of the Leray-Schauder Theorem
cites work: Q5608643
cites work: Q5671247
cites work: Fixed points in locally convex spaces

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Fixed points of condensing functions

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Q4146161

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Q3902047

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Fixpunktsätze vom Krasnoselski-Typ

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Q5767856

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Q5551837

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Q5640299

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Über die Methode der a priori-Schranken

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Neue Existenzsätze in der Theorie nichtlinearer Integralgleichungen

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Leray-Schauder Principles for Condensing Multi-Valued Mappings in Topological Linear Spaces

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Some fixed point theorems for multivalued mappings

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: A theorem on the minimization of a condensing multifunction and fixed points

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: A fixed point theorem, and some applications

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Some Fixed Point Theorems for Condensing Multifunctions in Locally Convex Spaces

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Fixed point theorems for condensing multivalued mappings on a locally convex topological space

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: Q5513450

Generalized Leray-Schauder principles for condensing admissible multifunctions (cites work)
cites work: The Ljusternik-Schnirelman theory for indefinite and not necessarily odd nonlinear operators and its applications