A TF-Contractive Fixed Point Theorem in a General Metric Space

2013 ◽  
Vol 671-674 ◽  
pp. 1628-1631
Author(s):  
Zong Hu Xiu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Generalized Metric Space ◽  
Generalized Metric

We establish a fixed point theorem in the generalized metric space introduced by M.oradi and Beiranvand for mapping satisfying a general contractive inequality. The obtained result can be considered as an extension of the theorem of Moradi and Beiranvand.

Kannan fixed point theorem on generalized metric space with a graph

2019 ◽  
Vol 13 (6) ◽  
pp. 263-274 ◽  
Author(s):  
Karim Chaira ◽  
Abderrahim Eladraoui ◽  
Mustapha Kabil ◽  
Abdessamad Kamouss
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Generalized Metric Space ◽  
Generalized Metric

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 Subordinate Semimetric Spaces and Fixed Point Theorems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
José Villa-Morales
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Generalized Metric Space ◽  
Generalized Metric ◽  
Semimetric Space ◽  
Semimetric Spaces ◽  
Matkowski’S Fixed Point Theorem

We introduce the concept of subordinate semimetric space. Such notion includes the concept of RS-space introduced by Roldán and Shahzad; therefore the concepts of Branciari’s generalized metric space and Jleli and Samet’s generalized metric space are particular cases. For such spaces we prove a version of Matkowski’s fixed point theorem, and introducing the concept of q-contraction we get a fixed point theorem of Kannan-Ćirić type. Moreover, using such result we characterize complete subordinate semimetric spaces.

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.

Fixed point theorems in generalized metric spaces

2016 ◽  
Vol 10 (02) ◽  
pp. 1750030
Author(s):  
Stefan Czerwik ◽  
Krzysztof Król
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Banach Fixed Point Theorem ◽  
Generalized Metric Space ◽  
Generalized Metric

In the paper, we shall prove the results on the existence of fixed points of mapping defined on generalized metric space satisfying a nonlinear contraction condition, which is a generalization of Diaz and Margolis theorem (see [A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968) 305–309]). We also present local fixed point theorems both in generalized and ordinary metric spaces. Our results are generalizations of Banach fixed point theorem and many other results.

Application of Perov’s fixed point theorem to Fredholm type integro-differential equations in two variables

2016 ◽  
Vol 66 (5) ◽  
Author(s):  
Asadollah Aghajani ◽  
Ehsan Pourhadi ◽  
Margarita Rivero ◽  
Juan J. Trujillo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Metric Space ◽  
Integrodifferential Equations ◽  
Generalized Metric Space ◽  
Fredholm Type ◽  
Generalized Metric

AbstractIn this paper, we consider the concept of the so-called generalized metric space and give some results on the existence, uniqueness and estimation of the solutions of Fredholm type integrodifferential equations in two variables using Perov’s fixed point theorem. Furthermore, we give some illustrative examples to verify the effectiveness and applicability of our main result.

scholarly journals Systems of implicit fractional fuzzy differential equations with nonlocal conditions

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3795-3822 ◽  
Author(s):  
Nguyen Son ◽  
Nguyen Dong
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Generalized Metric Space ◽  
Generalized Metric ◽  
Vector Version ◽  
Fuzzy Solutions

In this paper, two types of fixed point theorems are employed to study the solvability of nonlocal problem for implicit fuzzy fractional differential systems under Caputo gH-fractional differentiability in the framework of generalized metric spaces. First of all, we extend Krasnoselskii?s fixed point theorem to the vector version in the generalized metric space of fuzzy numbers. Under the Lipschitz conditions, we use Perov?s fixed point theorem to prove the global existence of the unique mild fuzzy solution in both types (i) and (ii). When the nonlinearity terms are not Lipschitz, we combine Perov?s fixed point theorem with vector version of Krasnoselskii?s fixed point theorem to prove the existence of mild fuzzy solutions. Based on the advantage of vector-valued metrics and convergent matrix, we attain some properties of mild fuzzy solutions such as the boundedness, the attractivity and the Ulam - Hyers stability. Finally, a computational example is presented to demonstrate the effectivity of our main results.

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