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 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 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 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.

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 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 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 Some fixed point results in complete generalized metric spaces

2018 ◽  
Vol 9 (2) ◽  
pp. 171-180
Author(s):  
S.M. Sangurlu ◽  
D. Turkoglu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Weak Contraction ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Banach Contraction

The Banach contraction principle is the most important result. This principle has many applications and some authors was interested in this principle in various metric spaces as Brianciari. The author initiated the notion of the generalized metric space as a generalization of a metric space by replacing the triangle inequality by a more general inequality, $d(x,y)\leq d(x,u)+d(u,v)+d(v,y)$ for all pairwise distinct points $x,y,u,v$ of $X$. As such, any metric space is a generalized metric space but the converse is not true. He proved the Banach fixed point theorem in such a space. Some authors proved different types of fixed point theorems by extending the Banach's result. Wardowski introduced a new contraction, which generalizes the Banach contraction. He using a mapping $F: \mathbb{R}^{+} \rightarrow \mathbb{R}$ introduced a new type of contraction called $F$-contraction and proved a new fixed point theorem concerning $F$-contraction. In this paper, we have dealt with $F$-contraction and $F$-weak contraction in complete generalized metric spaces. We prove some results for $F$-contraction and $F$-weak contraction and we show that the existence and uniqueness of fixed point for satisfying $F$-contraction and $F$-weak contraction in complete generalized metric spaces. Some examples are supplied in order to support the useability of our results. The obtained result is an extension and a generalization of many existing results in the literature.

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