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 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.

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.

scholarly journals A minimization theorem in quasi-metric spaces and its applications

2002 ◽  
Vol 31 (7) ◽  
pp. 443-447 ◽  
Author(s):  
Jeong Sheok Ume
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Caristi’S Fixed Point Theorem ◽  
Caristi's Fixed Point Theorem

We prove a new minimization theorem in quasi-metric spaces, which improves the results of Takahashi (1993). Further, this theorem is used to generalize Caristi's fixed point theorem and Ekeland'sϵ-variational principle.

scholarly journals Caristi’s Fixed Point Theorem in G-Metric Spaces and Applications

2021 ◽  
pp. 3-7
Author(s):  
Iluno C. ◽  
Adetowubo A. ◽  
Adewale O. K.
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Caristi’S Fixed Point Theorem ◽  
Good Number ◽  
Caristi's Fixed Point Theorem

In this paper, we give some versions of Caristi’s fixed point theorem in a more general metric spacesetting. Our work extends a good number of results in this area of research

Some fixed point theorems in partial \(S_b\)-metric spaces

2018 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Koushik Sarkar ◽  
Manoranjan Singha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
New Class ◽  
Contractive Mappings ◽  
Banach Contraction

N. Souayah [10] introduced the concept of partial Sb-metric spaces. In this paper, we established a fixed point theorem for a new class of contractive mappings and a generalization of Theorem 2 from [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Am. Math. Soc. 136, (2008), 1861-1869] in partial Sb-metric spaces. We provide an example in support of our result.

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.

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