scholarly journals Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Kazimierz Włodarczyk ◽  
Robert Plebaniak
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Dynamic Systems ◽  
Metric Spaces ◽  
Lower Semicontinuous ◽  
Type Theorem ◽  
Uniform Spaces ◽  
Asymmetric Structures ◽  
Symmetric Structures ◽  
Locally Convex

In uniform spacesX, Dwith symmetric structures determined by theD-families of pseudometrics which define uniformity in these spaces, the new symmetric and asymmetric structures determined by theJ-families of generalized pseudodistances onXare constructed; using these structures the set-valued contractions of two kinds of Nadler type are defined and the new and general theorems concerning the existence of fixed points and endpoints for such contractions are proved. Moreover, using these new structures, the single-valued contractions of two kinds of Banach type are defined and the new and general versions of the Banach uniqueness and iterate approximation of fixed point theorem for uniform spaces are established. Contractions defined and studied here are not necessarily continuous. One of the main key ideas in this paper is the application of our fixed point and endpoint version of Caristi type theorem for dissipative set-valued dynamic systems without lower semicontinuous entropies in uniform spaces with structures determined byJ-families. Results are new also in locally convex and metric spaces. Examples are provided.

scholarly journals Fixed point theorems for nonexpansive mappings in a locally convex space

1979 ◽  
Vol 20 (2) ◽  
pp. 179-186 ◽  
Author(s):  
P. Srivastava ◽  
S.C. Srivastava
Keyword(s):  
Fixed Point ◽  
Convex Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Uniform Space ◽  
Normal Structure ◽  
Locally Convex Space ◽  
Uniform Spaces ◽  
Locally Convex

Several fixed point theorems for nonexpansive self mappings in metric spaces and in uniform spaces are known. In this context the concept of orbital diameters in a metric space was introduced by Belluce and Kirk. The concept of normal structure was utilized earlier by Brodskiĭ and Mil'man. In the present paper, both these concepts have been extended to obtain definitions of β-orbital diameter and β-normal structure in a uniform space having β as base for the uniformity. The closed symmetric neighbourhoods of zero in a locally convex space determine a base β of a compatible uniformity. For 3-nonexpansive self mappings of a locally convex space, fixed point theorems have been obtained using the concepts of β-orbital diameter and β-normal structure. These theorems generalise certain theorems of Belluce and Kirk.

scholarly journals Maximality, fixed points and variational principles for mappings on quasi-uniform spaces

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5345-5355
Author(s):  
Raúl Fierro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Variational Principles ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniform Structure ◽  
Uniform Spaces ◽  
Order Relations ◽  
And Variational Principles

By making use of maximality on some appropriate preorderings, some classical results stated in the context of metric spaces are extended to spaces endowed with quasi-uniform structures. Indeed, various results on fixed point theory and variational principles have been proved by arguments using order relations in metric spaces. In this work, some of the mentioned results are extended to spaces having a quasi-uniform structure, by means of appropriate preorderings. The concept of w-distance is used to this purpose. Moreover, equivalences of maximality are stated for general preorderings.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

scholarly journals Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

BEST PROXIMITY POINTS AND FIXED POINTS WITH -FUNCTIONS IN THE FRAMEWORK OF -DISTANCES

2018 ◽  
Vol 99 (03) ◽  
pp. 497-507 ◽  
Author(s):  
ALEKSANDAR KOSTIĆ ◽  
ERDAL KARAPINAR ◽  
VLADIMIR RAKOČEVIĆ
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Best Proximity Points

We study best proximity points in the framework of metric spaces with $w$ -distances. The results extend, generalise and unify several well-known fixed point results in the literature.

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

scholarly journals Fuzzy fixed points of generalized F2-Geraghty type fuzzy mappings and complementary results

2016 ◽  
Vol 21 (2) ◽  
pp. 274-292 ◽  
Author(s):  
Mujahid Abbas ◽  
Basit Ali ◽  
Ornella Rizzo ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Computer Science ◽  
Fixed Points ◽  
Metric Space ◽  
Type Theorem ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Hybrid Pair ◽  
Fuzzy Fixed Point

The aim of this paper is to introduce generalized F2-Geraghty type fuzzy mappings on a metric space for establishing the existence of fuzzy fixed points of such mappings. As an application of our result, we obtain the existence of common fuzzy fixed point for a generalized F2-Geraghty type fuzzy hybrid pair. These results unify, generalize and complement various known comparable results in the literature. An example and an application to theoretical computer science are presented to support the theory proved herein. Also, to suggest further research on fuzzy mappings, a Feng–Liu type theorem is proved.

scholarly journals FIXED POINTS FOR TWO PAIRS OF ABSORBING MAPPINGS IN WEAK PARTIAL METRIC SPACES

2020 ◽  
pp. 283
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Partial Metric Spaces

In this paper, a general fixed point theorem for two pairs of absorbing mappings in weak partial metric space, using implicit relations, has been proved.

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