On Recent Results Concerning F-Contraction in Generalized Metric Spaces

In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce ( φ , F ) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping.

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Some new observations on fixed point results in rectangular metric spaces with applications to chemical sciences

Vojnotehnicki glasnik ◽

10.5937/vojtehg69-29517 ◽

2021 ◽

Vol 69 (1) ◽

pp. 8-30

Author(s):

Mudasir Younis ◽

Nicola Fabiano ◽

Zaid Fadail ◽

Zoran Mitrović ◽

Stojan Radenović

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Spaces ◽

Fixed Point Theory ◽

Nonlinear Problems ◽

Point Theory ◽

New Approach ◽

Generalized Metric Spaces ◽

Picard Sequence ◽

Open Question

Introduction/purpose: This paper considers, generalizes and improves recent results on fixed points in rectangular metric spaces. The aim of this paper is to provide much simpler and shorter proofs of some new results in rectangular metric spaces. Methods: Some standard methods from the fixed point theory in generalized metric spaces are used. Results: The obtained results improve the well-known results in the literature. The new approach has proved that the Picard sequence is Cauchy in rectangular metric spaces. The obtained results are used to prove the existence of solutions to some nonlinear problems related to chemical sciences. Finally, an open question is given for generalized contractile mappings in rectangular metric spaces. Conclusions: New results are given for fixed points in rectangular metric spaces with application to some problems in chemical sciences.

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A New Approach of Some Contractive Mappings on Metric Spaces

Mathematics ◽

10.3390/math9121433 ◽

2021 ◽

Vol 9 (12) ◽

pp. 1433

Author(s):

Ion Marian Olaru ◽

Nicolae Adrian Secelean

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Integral Equations ◽

Point Theorem ◽

Metric Spaces ◽

New Approach ◽

Type Mapping ◽

Contractive Mappings ◽

Contraction Type

In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated.

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SOME FIXED POINT THEOREMS FOR GENERALIZED $\alpha$-GERAGHTY CONTRACTION TYPE MAPPINGS IN $B$-METRIC~SPACES AND SOME APPLICATIONS TO THE NONLINEAR INTEGRAL EQUATION

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi1702231h ◽

2017 ◽

pp. 231

Author(s):

Nguyen Trung Hieu ◽

Le Thi Chac

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorems ◽

Nonlinear Integral Equation ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Generalized Metric Spaces ◽

Type Mapping ◽

Contraction Type

The purpose of this paper is to introduce the notion of a generalized $\alpha$-Geraghty contraction type mapping in $b$-metric~spaces and state the existence and uniqueness of a fixed point for this mapping. These results are generalizations of certain the main results in [D.~\DJ uki\'{c}, Z.~Kadelburg, and S.~Radenovi\'{c}, \emph{Fixed points of Geraghty-type mappings in various generalized metric spaces}, Abstr. Appl. Anal. \textbf{2011} (2011), 13 pages] and [O.~Popescu, \emph{ Some new fixed point theorems for $\alpha$-Geraghty contraction type maps in metric spaces}, Fixed Point Theory Appl. \textbf{2014:190} (2014), 1 -- 12]. Some examples are given to illustrate the obtained results and to show that these results are proper extensions of the existing ones. Then we apply the obtained theorem to study the existence of solutions to the nonlinear integral equation.

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Some related fixed point theorems for multivalued mappings on two metric spaces

Carpathian Mathematical Publications ◽

10.15330/cmp.12.2.392-400 ◽

2020 ◽

Vol 12 (2) ◽

pp. 392-400

Author(s):

Ö. Biçer ◽

M. Olgun ◽

T. Alyildiz ◽

I. Altun

Keyword(s):

Fixed Point ◽

Classical Result ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Multivalued Mappings ◽

Compact Set ◽

Complete Metric Spaces ◽

Bounded Set ◽

Contraction Type ◽

Definition Of

The definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via $F$-contraction type conditions.

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Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces

Axioms ◽

10.3390/axioms7040074 ◽

2018 ◽

Vol 7 (4) ◽

pp. 74 ◽

Cited By ~ 6

Author(s):

Haitham Qawaqneh ◽

Mohd Noorani ◽

Wasfi Shatanawi ◽

Habes Alsamir

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Partially Ordered ◽

Type Mapping ◽

Admissible Mapping ◽

Contraction Type ◽

Common Fixed Point Theorems

The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α − admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces.

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Common fixed point theorems without continuity and compatible property of maps

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v35i3.28636 ◽

2017 ◽

Vol 35 (3) ◽

pp. 67-77 ◽

Cited By ~ 3

Author(s):

Vinod Bhardwaj ◽

Vishal Gupta ◽

Naveen Mani

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Weak Contraction ◽

Integral Type ◽

Complete Metric Spaces ◽

Contraction Of Integral Type ◽

Common Fixed Point Theorems

In this paper, without assuming continuity, commutativity and compatibility of self maps, some common fixed theorem for weak contraction of integral type in complete metric spaces are proved. An example and some remarks are also given to justify that our contraction is new and weaker than other existing contractions.

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A New Approach to the Study of Fixed Point Theorems withw-Distances viaR-Functions

Journal of Function Spaces ◽

10.1155/2016/6978439 ◽

2016 ◽

Vol 2016 ◽

pp. 1-9

Author(s):

Farzad Zarinfar ◽

Farshid Khojasteh ◽

Seyyed Mansour Vaezpour

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

New Approach ◽

Complete Metric Spaces ◽

Type Contraction

We introduce some new generalization of fixed point theorems in complete metric spaces endowed withw-distances viaR-functions. Our results extend many of known fixed point theorems such as Reich type contraction, Geraghty contraction, Meir-Keeler contraction, andZ-contraction. In addition, the result and corollaries show that our approach has a constructive attitude and many known and unknown results can be constructed in such way.

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Fixed Points Of F-Weak Contractions On Complete Metric Spaces

Demonstratio Mathematica ◽

10.2478/dema-2014-0012 ◽

2014 ◽

Vol 47 (1) ◽

Cited By ~ 26

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

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Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

Annales Mathematicae Silesianae ◽

10.2478/amsil-2021-0003 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Kushal Roy ◽

Sayantan Panja ◽

Mantu Saha ◽

Zoran D. Mitrović

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Contractive Mapping ◽

Weak Contraction ◽

Complete Metric Spaces ◽

Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

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On Some New Jungck–Fisher–Wardowski Type Fixed Point Results

Symmetry ◽

10.3390/sym12122048 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2048

Author(s):

Jelena Vujaković ◽

Eugen Ljajko ◽

Slobodan Radojević ◽

Stojan Radenović

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

New Approach ◽

Complete Metric Spaces

Many authors used the concept of F−contraction introduced by Wardowski in 2012 in order to define and prove new results on fixed points in complete metric spaces. In some later papers (for example Proinov P.D., J. Fixed Point Theory Appl. (2020)22:21, doi:10.1007/s11784-020-0756-1) it is shown that conditions (F2) and (F3) are not necessary to prove Wardowski’s results. In this article we use a new approach in proving that the Picard–Jungck sequence is a Cauchy one. It helps us obtain new Jungck–Fisher–Wardowski type results using Wardowski’s condition (F1) only, but in a way that differs from the previous approaches. Along with that, we came to several new contractive conditions not known in the fixed point theory so far. With the new results presented in the article, we generalize, extend, unify and enrich methods presented in the literature that we cite.

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