scholarly journals Topological Transversality Coincidence Theory for Multivalued Maps with Selections in a Given Class

2021 ◽  
Vol 29 (1) ◽  
pp. 201-209
Author(s):  
Donal O’Regan
Keyword(s):  
Multivalued Maps ◽  
Coincidence Theory ◽  
Coincidence Theorem

Abstract This paper presents the topological transversality coincidence theorem for general multivalued maps who have selections in a given class of maps.

scholarly journals Maximal Type Elements for Families

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2269
Author(s):  
Donal O’Regan
Keyword(s):  
Real World ◽  
Existence Theorems ◽  
General Setting ◽  
Physical Models ◽  
Existence Theory ◽  
Type Result ◽  
Multivalued Maps ◽  
The Third ◽  
Coincidence Theory ◽  
Element Type

In this paper, we present a variety of existence theorems for maximal type elements in a general setting. We consider multivalued maps with continuous selections and multivalued maps which are admissible with respect to Gorniewicz and our existence theory is based on the author’s old and new coincidence theory. Particularly, for the second section we present presents a collectively coincidence coercive type result for different classes of maps. In the third section we consider considers majorized maps and presents a variety of new maximal element type results. Coincidence theory is motivated from real-world physical models where symmetry and asymmetry play a major role.

A coincidence theorem for multivalued maps and its applications

2013 ◽  
Vol 17 (2) ◽  
pp. 331-340
Author(s):  
Aram Arutyunov ◽  
Boris Gelman ◽  
Valeri Obukhovskii
Keyword(s):  
Multivalued Maps ◽  
Coincidence Theorem

scholarly journals Topological Transversality Principles and General Coincidence Theory

2017 ◽  
Vol 25 (2) ◽  
pp. 159-170 ◽  
Author(s):  
Donal O’Regan
Keyword(s):  
Topological Spaces ◽  
Multivalued Maps ◽  
Completely Regular ◽  
Coincidence Theory

AbstractThis paper presents general topological coincidence principles for multivalued maps defined on subsets of completely regular topological spaces.

scholarly journals Unified multivalued interpolative Reich–Rus–Ćirić-type contractions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Muhammad Usman Ali
Keyword(s):  
Fixed Point ◽  
Type Condition ◽  
Multivalued Maps ◽  
Contraction Type ◽  
Type Contraction

AbstractThis article examines new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions and fixed point results for multivalued maps that fulfill these conditions. Earlier defined interpolative contraction type conditions cannot be particularized to any contraction type condition. This slackness of the interpolative contraction type condition is addressed through new multivalued interpolative Reich–Rus–Ćirić-type contraction conditions.

On soft set-valued maps and integral inclusions

2021 ◽  
pp. 1-15
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fixed Point Theorems ◽  
Soft Set ◽  
Mathematical Tool ◽  
Multivalued Maps ◽  
Soft Sets ◽  
Special Cases ◽  
New Development

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.

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.

Selections of multivalued maps and shape domination

1990 ◽  
Vol 107 (3) ◽  
pp. 493-499 ◽  
Author(s):  
José M. R. Sanjurjo
Keyword(s):  
Multivalued Map ◽  
Shape Theory ◽  
Multivalued Maps

AbstractSome results are presented which establish connections between shape theory and the theory of multivalued maps. It is shown how to associate an upper-semi-continuous multivalued map F: X → Y to every approximative map f = {fk, X → Y} in the sense of K. Borsuk and it is proved that, in certain circumstances, if F is ‘small’ and admits a selection, then the shape morphism S(f) is generated by a map, and if F admits a coselection then S(f) is a shape domination.

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.

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