scholarly journals Only 3-generalized metric spaces have a compatible symmetric topology

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Tomonari Suzuki ◽  
Badriah Alamri ◽  
Misako Kikkawa
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric

AbstractWe prove that every 3-generalized metric space is metrizable. We also show that for any ʋ with ʋ ≥ 4, not every ʋ-generalized metric space has a compatible symmetric topology.

scholarly journals The Generalized Weaker(α-ϕ-φ)-Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Chi-Ming Chen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of generalized weaker(α-ϕ-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

scholarly journals Fixed point theorems for almost contractions in generalized metric spaces

2014 ◽  
Vol 23 (1) ◽  
pp. 65-72
Author(s):  
LULJETA KIKINA ◽  
◽  
KRISTAQ KIKINA ◽  
ILIR VARDHAMI ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Space Setting ◽  
Generalized Metric

Fixed point theorems for almost contractions in generalized metric spaces are proved. The obtained results are extensions and generalizations, from metric space setting to generalized metric space setting, of many well-known fixed point theorems in literature.

scholarly journals Pseudo Picard operators on generalized metric spaces

2018 ◽  
Vol 12 (2) ◽  
pp. 389-400 ◽  
Author(s):  
Ishak Altun ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
New Class ◽  
Generalized Metric

In this paper, we present a new class of pseudo Picard operators in the setting of generalized metric spaces introduced recently in [M. Jleli and B. Samet: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., (2015) 2015:61]. An example is provided to illustrate the main result.

scholarly journals Porosity of certain classes of operators in generalized metric spaces

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Pratulananda Das ◽  
Lakshmi Kanta Dey
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

AbstractWe study the porosity behavior of non-contractive mappings in a generalized metric space, a concept recently introduced in [

A new contribution to the fixed point theory in b-generalized metric spaces

2017 ◽  
Vol 8 (1) ◽  
pp. 111
Author(s):  
Ahmed H. Soliman ◽  
M. A. Ahmed ◽  
A. M. Zidan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Rational Type

In this work, we introduce a new generalized metric space called b-generalized metric spaces (shortly, b-G.M.S). Also, we establish some fixed point results for a contraction of rational type in b-G.M.S. Some interesting examples are also given.

scholarly journals Fisher Fixed Point Results in Generalized Metric Spaces with a Graph

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Karim Chaira ◽  
Abderrahim Eladraoui ◽  
Mustapha Kabil ◽  
Abdessamad Kamouss
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Banach Contraction

We discuss Fisher’s fixed point theorem for mappings defined on a generalized metric space endowed with a graph. This work should be seen as a generalization of the classical Fisher fixed point theorem. It extends some recent works on the enlargement of Banach Contraction Principle to generalized metric spaces with graph. An example is given to illustrate our result.

scholarly journals Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 134 ◽  
Author(s):  
Bucur
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Existence Theorems ◽  
Real Life ◽  
Generalized Metric Space ◽  
Weighted Mean ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
New Concepts

This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains not only an example of application in science, but also an example of application in real life, in biology, in order to find an equilibrium solution to a prey–predator-type problem. The results of this paper extend theorems for multivalued left-weighted mean contractions in the generalized sense of Nadler, demonstrating that some of the results given by Rus (2008), Mureșan (2002), and Nadler (1969) in metric spaces can also be proved in symmetric generalized metric spaces.

scholarly journals A fixed point theorem in generalized metric spaces

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Luljeta Kikina ◽  
Kristaq Kikina
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric

AbstractA generalized metric space has been defined by Branciari as a metric space in which the triangle inequality is replaced by a more general inequality. Subsequently, some classical metric fixed point theorems have been transferred to such a space. In this paper, we continue in this direction and prove a version of Fisher’s fixed point theorem in generalized metric spaces.

scholarly journals so-metrizable spaces and images of metric spaces

2021 ◽  
Vol 19 (1) ◽  
pp. 1145-1152
Author(s):  
Songlin Yang ◽  
Xun Ge
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Metrizable Space ◽  
Open Mapping ◽  
Generalized Metric Space ◽  
Locally Finite ◽  
Generalized Metric Spaces ◽  
Covering Mapping ◽  
Generalized Metric ◽  
Metrizable Spaces

Abstract so-metrizable spaces are a class of important generalized metric spaces between metric spaces and s n sn -metrizable spaces where a space is called an so-metrizable space if it has a σ \sigma -locally finite so-network. As the further work that attaches to the celebrated Alexandrov conjecture, it is interesting to characterize so-metrizable spaces by images of metric spaces. This paper gives such characterizations for so-metrizable spaces. More precisely, this paper introduces so-open mappings and uses the “Pomomarev’s method” to prove that a space X X is an so-metrizable space if and only if it is an so-open, compact-covering, σ \sigma -image of a metric space, if and only if it is an so-open, σ \sigma -image of a metric space. In addition, it is shown that so-open mapping is a simplified form of s n sn -open mapping (resp. 2-sequence-covering mapping if the domain is metrizable). Results of this paper give some new characterizations of so-metrizable spaces and establish some equivalent relations among so-open mapping, s n sn -open mapping and 2-sequence-covering mapping, which further enrich and deepen generalized metric space theory.

Generalized metric spaces are paracompact

1975 ◽  
Vol 77 (2) ◽  
pp. 325-326
Author(s):  
D. J. Souppouris
Keyword(s):  
Abelian Group ◽  
Metric Space ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
The Subject

A generalized metric space is a triple (X, d, G), where X is a set, G an ordered Abelian group and d: X x X → G is a function which satisfies the metric axioms. The generalized metric d defines a topology on X in the same way as an ordinary metric does for a metric space. These spaces are studied by Stevenson & Ton(5) and Sikorski (4) amongst others. A survey of these spaces is the subject of an M.Phil. thesis by the author (6). Generalized metric spaces satisfy most of the separation properties of ordinary metric spaces (T2, regular, etc.). We prove here that these spaces are also paracompact. The proof is a generalization of the proof given by Ruffin (2) for metric spaces. The result given here follows, in fact, from a theorem proved by Hayes (1). He proved that uniformities with totally ordered bases have paracompact topologies. It is known (Stevenson & Ton (5); Shock (3); Souppouris (6), chapter 5) that these spaces are identical to generalized metric spaces. The proof given here uses metric space language.

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