Porosity of certain classes of operators in generalized metric spaces

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.

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Periodic and fixed point using weaker Meir-Keeler function in complete generalized metric spaces

Filomat ◽

10.2298/fil1608191n ◽

2016 ◽

Vol 30 (8) ◽

pp. 2191-2206

Author(s):

Hemant Nashine ◽

Hossein Lakzian

Keyword(s):

Fixed Point ◽

Metric Space ◽

Metric Spaces ◽

Existence Results ◽

Generalized Metric Space ◽

Generalized Metric Spaces ◽

Contractive Mappings ◽

Generalized Metric

We originate some existence results on periodic and fixed point using generalized (???)- contractions and generalized (?,?)-contractive mappings with weaker Meir-Keeler function in the setup of a complete generalized metric space in sense of Branciari without Hausdorff assumption. Our results generalize the results of several well-known comparable results in the literature. To illustrate our results, we conclude the paper with some examples.

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Fixed Point Results for C -Contractive Mappings in Generalized Metric Spaces with a Graph

Journal of Function Spaces ◽

10.1155/2021/8840347 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Karim Chaira ◽

Mustapha Kabil ◽

Abdessamad Kamouss

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Generalized Metric Space ◽

Matrix Equations ◽

Generalized Metric Spaces ◽

Contraction Mappings ◽

Contractive Mappings ◽

Generalized Metric

In this paper, we establish fixed point theorems for Chatterjea contraction mappings on a generalized metric space endowed with a graph. Our results extend, generalize, and improve many of existing theorems in the literature. Moreover, some examples and an application to matrix equations are given to support our main result.

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Fixed point theorems for almost contractions in generalized metric spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2014.01.05 ◽

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.

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Pseudo Picard operators on generalized metric spaces

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm170105008a ◽

2018 ◽

Vol 12 (2) ◽

pp. 389-400 ◽

Cited By ~ 1

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.

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

Journal of Advanced Studies in Topology ◽

10.20454/jast.2017.1334 ◽

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.

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Fisher Fixed Point Results in Generalized Metric Spaces with a Graph

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2020/7253759 ◽

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.

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

Symmetry ◽

10.3390/sym12010134 ◽

2020 ◽

Vol 12 (1) ◽

pp. 134 ◽

Cited By ~ 1

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.

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A fixed point theorem in generalized metric spaces

Demonstratio Mathematica ◽

10.1515/dema-2013-0432 ◽

2013 ◽

Vol 46 (1) ◽

Cited By ~ 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.

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so-metrizable spaces and images of metric spaces

Open Mathematics ◽

10.1515/math-2021-0082 ◽

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.

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