Coincidence results and Leray–Schauder alternatives between multivalued maps with continuous selections and admissible maps

2020 ◽  
Vol 284 ◽  
pp. 107368
Author(s):  
Donal O'Regan
Keyword(s):  
Multivalued Maps ◽  
Continuous Selections ◽  
Admissible Maps

Chaos for Differential Equations with Multivalued Impulses

2021 ◽  
Vol 31 (07) ◽  
pp. 2150113
Author(s):  
Jan Andres
Keyword(s):  
Differential Equations ◽  
Topological Entropy ◽  
Deterministic Chaos ◽  
Impulsive Differential Equations ◽  
Multivalued Maps ◽  
Nielsen Numbers ◽  
Positive Topological Entropy ◽  
Translation Operators ◽  
Principal Tool ◽  
Admissible Maps

The deterministic chaos in the sense of a positive topological entropy is investigated for differential equations with multivalued impulses. Two definitions of topological entropy are examined for three classes of multivalued maps: [Formula: see text]-valued maps, [Formula: see text]-maps and admissible maps in the sense of Górniewicz. The principal tool for its lower estimates and, in particular, its positivity are the Ivanov-type inequalities in terms of the asymptotic Nielsen numbers. The obtained results are then applied to impulsive differential equations via the associated Poincaré translation operators along their trajectories. The main theorems for chaotic differential equations with multivalued impulses are formulated separately on compact subsets of Euclidean spaces and on tori. Several illustrative examples are supplied.

FIXED POINT THEOREMS FOR GENERAL CLASSES OF MAPS ACTING ON TOPOLOGICAL VECTOR SPACES

2011 ◽  
Vol 04 (03) ◽  
pp. 373-387 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Mohamed-Aziz Taoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Vector Spaces ◽  
Compact Sets ◽  
Multivalued Maps ◽  
Weakly Compact ◽  
Topological Vector Spaces ◽  
Admissible Maps ◽  
Weakly Compact Sets ◽  
Locally Convex

We present new fixed point theorems for multivalued [Formula: see text]-admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray–Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

scholarly journals The Topological Transversality Theorem for Multivalued Maps with Continuous Selections

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1113 ◽  
Author(s):  
Donal O’Regan
Keyword(s):  
The Other ◽  
Multivalued Maps ◽  
Continuous Selections ◽  
Transversality Theorem

This paper considers a topological transversality theorem for multivalued maps with continuous, compact selections. Basically, this says, if we have two maps F and G with continuous compact selections and F ≅ G , then one map being essential guarantees the essentiality of the other map.

scholarly journals Coincidence Theory in the Coercive Case and Minimax Inequalities

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1220
Author(s):  
Donal O’Regan
Keyword(s):  
Minimax Inequalities ◽  
Continuous Selections ◽  
Coincidence Theory ◽  
Admissible Maps

We established coincidence results between maps with continuous selections and admissible maps. Both the compact and coercive cases were considered, and our argument relied on new coincidence ideas established recently by the author. Using our coincidence theory, we established new analytic alternatives, which then generate new minimax inequalities of the Neumann–Sion type.

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.

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