scholarly journals Fixed point results for F-contractive mappings of Hardy-Rogers-type

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 715-722 ◽  
Author(s):  
Monica Cosentino ◽  
Pasquale Vetroa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Banach Contraction

Recently, Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for self-mappings on complete metric spaces or complete ordered metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.

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 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 A generalization of Nadler fixed point theorem

2015 ◽  
Vol 31 (3) ◽  
pp. 403-410
Author(s):  
FRANCESCA VETRO ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Multivalued Mappings ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Jleli and Samet gave a new generalization of the Banach contraction principle in the setting of Branciari metric spaces [Jleli, M. and Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014:38 (2014)]. The purpose of this paper is to study the existence of fixed points for multivalued mappings, under a similar contractive condition, in the setting of complete metric spaces. Some examples are provided to illustrate the new theory.

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.

scholarly journals Fixed point theorems for multivalued generalized contractions of rational type in complete metric spaces

2014 ◽  
Vol 23 (1) ◽  
pp. 99-106
Author(s):  
ANCA M. OPREA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Multivalued Operators ◽  
Multivalued Contractions ◽  
Rational Type

The purpose of this paper is to present some fixed point theorems for multivalued contractions of rational type. We extend the results of I. Cabrera, J. Harjani and K. Sadarangan, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Annali dellUniversita di Ferrara, DOI 10.1007/s11565-013-0176-x, to the case of multivalued operators.

scholarly journals Multi-valued F-contractions and the solutions of certain functional and integral equations

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1259-1268 ◽  
Author(s):  
Margherita Sgroi ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Banach Contraction

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

Some deterministic and random fixed point theorems on a graph

2018 ◽  
Vol 26 (4) ◽  
pp. 211-224 ◽  
Author(s):  
Juan J. Nieto ◽  
Abdelghani Ouahab ◽  
Rosana Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Random Fixed Point ◽  
Ordered Metric Spaces ◽  
Banach Contraction

Abstract We present the random version of the classical Banach contraction principle and some of its generalizations to ordered metric spaces or in metric spaces endowed with a graph.

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