scholarly journals Remarks of Fixed Point for ( ψ , φ )-Weakly Contractive Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Zhiqun Xue ◽  
Guiwen Lv
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Generalized Metric Spaces ◽  
Contraction Mappings ◽  
Contractive Mappings ◽  
Weakly Contractive ◽  
Appl Math

In this paper, we obtain a new fixed point theorem for weak contraction mappings on complete generalized metric spaces. Our result is different from that of ( ψ , φ )-weakly contractive mappings which had been obtained by Lakzian–Samet’s [Appl. Math. Lett. 25 (2012) 902–906]. Moreover, an example is given to illustrate the usability of the obtained result.

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 A fixed point theorem for generalized weakly contractive mappings in b -metric spaces

2020 ◽  
Vol 4 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Eliyas Zinab ◽  
◽  
Kidane Koyas ◽  
Aynalem Girma ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Weakly Contractive

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.

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.

scholarly journals On ParametricS-Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Nihal Taş ◽  
Nihal Yılmaz Özgür
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Point Type

We introduce the notion of a parametricS-metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametricS-metric space. It is important to obtain new fixed-point theorems on a parametricS-metric space because there exist some parametricS-metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametricS-metric space.

scholarly journals (α,ψ)-Meir-Keeler Contraction Mappings in Generalized b-Metric Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Erdal Karapinar ◽  
Stefan Czerwik ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contraction Mappings

We present a fixed point theorem for generalized (α,ψ)-Meir-Keeler type contractions in the setting of generalized b-metric spaces. The presented results improve, generalize, and unify many existing famous results in the corresponding literature.

scholarly journals Fixed Points Of F-Weak Contractions On Complete Metric Spaces

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
D. Wardowski ◽  
N. Van Dung
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Proper Extension

AbstractIn this paper, we introduce the notion of an F-weak contraction and prove a fixed point theorem for F-weak contractions. Examples are given to show that our result is a proper extension of some results known in the literature

scholarly journals Suzuki-Type Generalization of Chatterjea Contraction Mappings on Complete Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Mohammad Imdad ◽  
Ali Erduran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Partial Metric ◽  
Contraction Mappings ◽  
Partial Metric Spaces

Motivated by Suzuki (2008), we prove a Suzuki-type fixed point theorem employing Chatterjea contraction on partial metric spaces.

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