Fixed Points of Multivalued Maps

1986 ◽  
pp. 447-472 ◽  
Author(s):  
Eberhard Zeidler
Keyword(s):  
Fixed Points ◽  
Multivalued Maps

scholarly journals Applications of Coupled Fixed Points for Multivalued Maps in the Equilibrium in Duopoly Markets and in Aquatic Ecosystems

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 44
Author(s):  
Gana Gecheva ◽  
Miroslav Hristov ◽  
Diana Nedelcheva ◽  
Margarita Ruseva ◽  
Boyan Zlatanov
Keyword(s):  
Fixed Points ◽  
Aquatic Ecosystems ◽  
Market Equilibrium ◽  
Multivalued Maps ◽  
New Class ◽  
Wide Range ◽  
Coupled Fixed Points ◽  
Ordered Pairs ◽  
Duopoly Markets

We have obtained a new class of ordered pairs of multivalued maps that have pairs of coupled fixed points. We illustrate the main result with two examples that cover a wide range of models. We apply the main result in models in duopoly markets to get a market equilibrium and in aquatic ecosystems, also to get an equilibrium.

scholarly journals Common fixed points of single-valued and multivalued maps

2005 ◽  
Vol 2005 (19) ◽  
pp. 3045-3055 ◽  
Author(s):  
Yicheng Liu ◽  
Jun Wu ◽  
Zhixiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Partial Answer ◽  
Multivalued Maps ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems

We define a new property which contains the property (EA) for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. Our results extend previous ones. As an application, we give a partial answer to the problem raised by Singh and Mishra.

On Fixed Points of Acyclic Type Multivalued Maps

2017 ◽  
Vol 225 (4) ◽  
pp. 565-574
Author(s):  
B. D. Gel’man ◽  
V. V. Obukhovskii
Keyword(s):  
Fixed Points ◽  
Multivalued Maps

scholarly journals Fixed points and selections of set-valued maps on spaces with convexity

2000 ◽  
Vol 24 (9) ◽  
pp. 595-612 ◽  
Author(s):  
Peter Saveliev
Keyword(s):  
Fixed Points ◽  
Generalized Convexity ◽  
Vector Spaces ◽  
Multivalued Maps ◽  
Topological Vector Spaces ◽  
Selection Theorems ◽  
Locally Convex

We provide theorems extending both Kakutani and Browder fixed points theorems for multivalued maps on topological vector spaces, as well as some selection theorems. For this purpose we introduce convex structures more general than those of locally convex and non-locally convex topological vector spaces or generalized convexity structures due to Michael, van de Vel, and Horvath.

scholarly journals Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

2002 ◽  
Vol 30 (10) ◽  
pp. 627-635 ◽  
Author(s):  
S. L. Singh ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Multivalued Maps

It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

Fixed points of multivalued maps under local Lipschitz conditions and applications

2019 ◽  
Vol 150 (3) ◽  
pp. 1467-1494
Author(s):  
Claudio A. Gallegos ◽  
Hernán R. Henríquez
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Abstract Cauchy Problem ◽  
Point Theory ◽  
Vector Subspace ◽  
Multivalued Maps ◽  
Lipschitz Continuous

AbstractIn this work we are concerned with the existence of fixed points for multivalued maps defined on Banach spaces. Using the Banach spaces scale concept, we establish the existence of a fixed point of a multivalued map in a vector subspace where the map is only locally Lipschitz continuous. We apply our results to the existence of mild solutions and asymptotically almost periodic solutions of an abstract Cauchy problem governed by a first-order differential inclusion. Our results are obtained by using fixed point theory for the measure of noncompactness.

Fixed points of Edelstein-type multivalued maps

2014 ◽  
Vol 63 (3) ◽  
pp. 399-407 ◽  
Author(s):  
Nayyar Mehmood ◽  
Akbar Azam ◽  
Ismat Beg
Keyword(s):  
Fixed Points ◽  
Multivalued Maps

scholarly journals Some Results on the Approximation of Solutions of Variational Inequalities for Multivalued Maps on Banach Spaces

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Luigi Muglia ◽  
Giuseppe Marino
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces ◽  
Unique Solution ◽  
Nonexpansive Mappings ◽  
Multivalued Maps ◽  
Demiclosedness Principle

AbstractMultivalued $$*$$ ∗ -nonexpansive mappings are studied in Banach spaces. The demiclosedness principle is established. Here we focus on the problem of solving a variational inequality which is defined on the set of fixed points of a multivalued $$*$$ ∗ -nonexpansive mapping. For this purpose, we introduce two algorithms approximating the unique solution of the variational inequality.

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