scholarly journals Characterization of  ∑-Semicompleteness via Caristi’s Fixed Point Theorem in Semimetric Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Tomonari Suzuki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach Contraction Principle ◽  
Caristi’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Semimetric Spaces ◽  
The Banach Contraction Principle ◽  
Caristi's Fixed Point Theorem

Introducing the concept of ∑-semicompleteness in semimetric spaces, we extend Caristi’s fixed point theorem to ∑-semicomplete semimetric spaces. Via this extension, we characterize ∑-semicompleteness. We also give generalizations of the Banach contraction principle.

scholarly journals Wardowski Type Characterization of the Interpolative Berinde Weak Fixed Point Theorem

2020 ◽  
pp. 411-414
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Weak Contraction ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In [1], Wardowski introduced the F-contractions, and used it to prove the Banach contraction principle. In this paper we introduce a concept of F-interpolative Berinde weak contraction, and use it to prove the interpolative Berinde weak mapping theorem of [2].

scholarly journals Caristi Fixed Point Theorem in Metric Spaces with a Graph

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
M. R. Alfuraidan ◽  
M. A. Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Caristi’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Caristi's Fixed Point Theorem

We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.

scholarly journals On the Correlation between Banach Contraction Principle and Caristi’s Fixed Point Theorem in b-Metric Spaces

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 136
Author(s):  
Salvador Romaguera
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Caristi’S Fixed Point Theorem ◽  
Contractivity Condition ◽  
Banach Contraction ◽  
Caristi's Fixed Point Theorem

We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper “A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces”. We also characterize the completeness of b-metric spaces with the help of a variant of the contractivity condition introduced by the authors in the aforementioned article.

scholarly journals On Caristi’s fixed point theorem in metric spaces with a graph

2020 ◽  
Vol 36 (2) ◽  
pp. 259-268
Author(s):  
NANTAPORN CHUENSUPANTHARAT ◽  
DHANANJAY GOPAL ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Caristi’S Fixed Point Theorem ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Caristi's Fixed Point Theorem

We generalize the Caristi’s fixed point theorem for single valued as well as multivalued mappings defined on ametric space endowed with a graph andw-distance. Particularly, we modify the concept of the (OSC)-propertydue to Alfuraidan and Khamsi (Alfuraidan M. R. and Khamsi, M. A.,Caristi fixed point theorem in metric spaceswith graph, Abstr. Appl. Anal., (2014) Art. ID 303484, 5.) which enable us to reformulated their stated graphtheory version theorem (Theorem 3.2 in Alfuraidan M. R. and Khamsi, M. A.,Caristi fixed point theorem in metricspaces with graph, Abstr. Appl. Anal., (2014) Art. ID 303484, 5. ) to the case ofw-distance. Consequently,we extend and improve some recent works concerning extension of Banach Contraction Theorem tow-distancewith graph e.g. (Jachymski, J.,The contraction principle for mappings on a metric space with graph, Proc. Amer. Math.Soc.,136(2008), No. 4, 1359–1373; Nieto, J. J., Pouso, R. L. and Rodriguez-Lopez R.,Fixed point theorems in orderedabstract spaces, Proc. Amer. Math. Soc.,135(2007), 2505–2517 and Petrusel, A. and Rus, I.,Fixed point theorems inorderedL−spaces endowed with graph, Proc. Amer, Math. Soc.,134(2006), 411–418.

scholarly journals New Fixed Point Theorems for θ ‐ ϕ -Contraction on Rectangular b -Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The Banach contraction principle is the most celebrated fixed point theorem and has been generalized in various directions. In this paper, inspired by the concept of θ ‐ ϕ -contraction in metric spaces, introduced by Zheng et al., we present the notion of θ ‐ ϕ -contraction in b -rectangular metric spaces and study the existence and uniqueness of a fixed point for the mappings in this space. Our results improve many existing results.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

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