scholarly journals Knaster-Kuratowski-Mazurkiewicz Theorem in Generalized Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Nayyar Mehmood ◽  
Israr Ali Khan ◽  
Haris Latif ◽  
Niaz Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fixed Points ◽  
Existence Result ◽  
Metric Spaces ◽  
Fractional Boundary Value Problem ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Kkm Mappings

We study Knaster-Kuratowski-Mazurkiewicz theorem in the setting of generalized metric spaces. We establish some results on fixed points of Knaster-Kuratowski-Mazurkiewicz (KKM) mappings. Fan’s matching and Schauder’s type fixed point theorem in generalized metric spaces are also proved as interesting consequences of our main results. Examples are given to validate our results. We use these results to prove existence result for a given Atangana-Baleanu-Caputo fractional boundary value problem.

Fixed point theorems for a system of transformations in generalized metric spaces

2015 ◽  
Vol 08 (04) ◽  
pp. 1550068 ◽  
Author(s):  
Stefan Czerwik ◽  
Krzysztof Król
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Fixed Point Theorem ◽  
Generalized Metric Spaces ◽  
Generalized Metric

In this paper we present the results on the existence of fixed points of system of mappings in generalized metric spaces generalizing the result of Diaz and Margolis. Also the “local fixed point theorems” of a system of such mappings both in generalized and ordinary metric spaces are stated. Banach fixed point theorem and many others are consequences of our results.

scholarly journals A fixed point theorem for generalized $(\psi ,\varphi )$-weak contractions in Branciari type generalized metric spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhiqun Xue ◽  
Guiwen Lv
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Convergence Theorem ◽  
Metric Spaces ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Weaker Conditions

AbstractIn this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.

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.

scholarly journals A fixed point theorem for generalized metric spaces

1996 ◽  
Vol 19 (3) ◽  
pp. 457-460 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Spaces ◽  
Generalized Metric

In this paper we prove two fixed point theorems for the generalized metric spaces introduced by Dhage.

Fixed point of contractive mappings in generalized metric spaces

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
Pratulananda Das ◽  
Lakshmi Dey
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

AbstractWe prove a fixed point theorem for contractive mappings of Boyd and Wong type in generalized metric spaces, a concept recently introduced in [BRANCIARI, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37].

scholarly journals Fixed Point Theorems for L-Contractions in Generalized Metric Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Seong-Hoon Cho
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Spaces ◽  
Generalized Metric

In this paper, the notion of L-contractions is introduced and a new fixed point theorem for such contractions is established.

scholarly journals Periodic Points and Fixed Points for the Weaker(ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Chi-Ming Chen ◽  
W. Y. Sun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Periodic Points ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of weaker(ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

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 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 Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces

2018 ◽  
Vol 19 (2) ◽  
pp. 189 ◽  
Author(s):  
Mortaza Abtahi ◽  
Zoran Kadelburg ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Partially Ordered ◽  
Generalized Metric ◽  
Coupled Fixed Points

<p>New fixed point and coupled fixed point theorems in partially ordered ν-generalized metric spaces are presented. Since the product of two ν-generalized metric spaces is not in general a ν-generalized metric space, a different approach is needed than in the case of standard metric spaces.</p>

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