On fixed points of asymptotically regular mappings

2020 ◽  
Author(s):  
Luong V. Nguyen
Keyword(s):  
Fixed Points ◽  
Asymptotically Regular

scholarly journals Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 411
Author(s):  
Pradip Debnath ◽  
Manuel de La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
The Other ◽  
Broad Category ◽  
Set Valued Mappings ◽  
Metric Function ◽  
Asymptotically Regular

The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous and asymptotically regular mappings in the set-valued context. We introduce two new contractive inequalities one of which is of Geraghty-type and the other is of Boyd and Wong-type. We proved two new existence of fixed point results corresponding to those inequalities.

scholarly journals On Fixed Points of Asymptotically Regular Mappings

1987 ◽  
Vol 43 (3) ◽  
pp. 328-346 ◽  
Author(s):  
B. E. Rhoades ◽  
S. sessa ◽  
M. S. Khan ◽  
M. Swaleh
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Linear Spaces ◽  
Complete Metric Spaces ◽  
Normed Linear Spaces ◽  
Asymptotically Regular

Some results on fixed points of asymptotically regular mappings are obtained in complete metric spaces and normed linear spaces.The structure of the set of common fixed points is also discussed in Banach spaces. Our work generalizes essentially known results of Das and Naik, Fisher, Jaggi, Jungck, Rhoades, Singh and Tiwari and several others.

Opial modulus, moduli of noncompact convexity and fixed points for asymptotically regular mappings

2000 ◽  
Vol 41 (5-6) ◽  
pp. 617-630 ◽  
Author(s):  
T.Domı́nguez Benavides ◽  
M.A.Japón Pineda
Keyword(s):  
Fixed Points ◽  
Asymptotically Regular

scholarly journals Uniform asymptotic normal structure, the uniform semi-Opial property, and fixed points of asymptotically regular uniformly lipschitzian semigroups. Part II

1998 ◽  
Vol 3 (3-4) ◽  
pp. 247-263
Author(s):  
Monika Budzyńska ◽  
Tadeusz Kuczumow ◽  
Simeon Reich
Keyword(s):  
Fixed Points ◽  
Normal Structure ◽  
Common Fixed Points ◽  
Opial Property ◽  
Asymptotic Normal ◽  
Asymptotically Regular

In this part of our paper we present several new theorems concerning the existence of common fixed points of asymptotically regular uniformly lipschitzian semigroups.

scholarly journals Fixed Points of Some Asymptotically Regular Multivalued Mappings Satisfying a Kannan-Type Condition

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 24
Author(s):  
Pradip Debnath ◽  
Zoran D. Mitrović ◽  
Hari Mohan Srivastava
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Type Condition ◽  
Asymptotically Regular

In this paper, we establish some existence of fixed-point results for some asymptotically regular multivalued mappings satisfying Kannan-type contractive condition without assuming compactness of the underlying metric space or continuity of the mapping.

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