Axioms

Research

8 pages, 225 KiB

Open AccessArticle

Viscosity Approximation Methods for * −Nonexpansive Multi-Valued Mappings in Convex Metric Spaces

by Azadeh Ghanifard, Hashem Parvaneh Masiha, Manuel De La Sen and Maryam Ramezani

Axioms 2020, 9(1), 10; https://doi.org/10.3390/axioms9010010 - 17 Jan 2020

Cited by 2 | Viewed by 1842

Abstract

In this paper, we prove convergence theorems for viscosity approximation processes involving

*

−nonexpansive multi-valued mappings in complete convex metric spaces. We also consider finite and infinite families of such mappings and prove convergence of the proposed iteration schemes to common fixed points [...] Read more.

In this paper, we prove convergence theorems for viscosity approximation processes involving

*

−nonexpansive multi-valued mappings in complete convex metric spaces. We also consider finite and infinite families of such mappings and prove convergence of the proposed iteration schemes to common fixed points of them. Our results improve and extend some corresponding results. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

21 pages, 316 KiB

Open AccessArticle

Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications

by Mohamed Amine Farid, Karim Chaira, El Miloudi Marhrani and Mohamed Aamri

Axioms 2019, 8(4), 130; https://doi.org/10.3390/axioms8040130 - 14 Nov 2019

Cited by 2 | Viewed by 2551

Abstract

In this paper, we prove some fixed point theorems for the nonlinear operator

A \cdot B + C

in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the [...] Read more.

In this paper, we prove some fixed point theorems for the nonlinear operator

A \cdot B + C

in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the application of our results to a nonlinear integral equation in Banach algebra. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

13 pages, 261 KiB

Open AccessArticle

Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

by Thenmozhi Shanmugam, Marudai Muthiah and Stojan Radenović

Axioms 2019, 8(4), 129; https://doi.org/10.3390/axioms8040129 - 14 Nov 2019

Cited by 8 | Viewed by 2172

Abstract

In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results. [...] Read more.

In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

14 pages, 263 KiB

Open AccessArticle

Informal Complete Metric Space and Fixed Point Theorems

by Hsien-Chung Wu

Axioms 2019, 8(4), 126; https://doi.org/10.3390/axioms8040126 - 07 Nov 2019

Viewed by 2070

Abstract

The concept of informal vector space is introduced in this paper. In informal vector space, the additive inverse element does not necessarily exist. The reason is that an element in informal vector space which subtracts itself cannot be a zero element. An informal [...] Read more.

The concept of informal vector space is introduced in this paper. In informal vector space, the additive inverse element does not necessarily exist. The reason is that an element in informal vector space which subtracts itself cannot be a zero element. An informal vector space can also be endowed with a metric to define a so-called informal metric space. The completeness of informal metric space can be defined according to the similar concept of a Cauchy sequence. A new concept of fixed point and the related results are studied in informal complete metric space. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

4 pages, 202 KiB

Open AccessArticle

A New Approach to the Interpolative Contractions

by Yaé Ulrich Gaba and Erdal Karapınar

Axioms 2019, 8(4), 110; https://doi.org/10.3390/axioms8040110 - 10 Oct 2019

Cited by 47 | Viewed by 2658

Abstract

We propose a refinement in the interpolative approach in fixed-point theory. In particular, using this method, we prove the existence of fixed points and common fixed points for Kannan-type contractions and provide examples to support our results. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

18 pages, 345 KiB

Open AccessArticle

C^*-Algebra Valued Fuzzy Soft Metric Spaces and Results for Hybrid Pair of Mappings

by Daripally Ram Prasad, Gajula Naveen Venkata Kishore, Hüseyin Işık, Bagathi Srinuvasa Rao and Gorantla Adi Lakshmi

Axioms 2019, 8(3), 99; https://doi.org/10.3390/axioms8030099 - 16 Aug 2019

Cited by 5 | Viewed by 2674

Abstract

In this paper, we establish some results on coincidence point and common fixed point theorems for a hybrid pair of single valued and multivalued mappings in complete

C^{*}

-algebra valued fuzzy soft metric spaces. In addition, we provided some coupled fixed point [...] Read more.

In this paper, we establish some results on coincidence point and common fixed point theorems for a hybrid pair of single valued and multivalued mappings in complete

C^{*}

-algebra valued fuzzy soft metric spaces. In addition, we provided some coupled fixed point theorems. Finally, we have given examples which support our main results. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

8 pages, 240 KiB

Open AccessArticle

Relatively Cyclic and Noncyclic P-Contractions in Locally K-Convex Space

by Edraoui Mohamed, Aamri Mohamed and Lazaiz Samih

Axioms 2019, 8(3), 96; https://doi.org/10.3390/axioms8030096 - 06 Aug 2019

Cited by 4 | Viewed by 2503

Abstract

Our main goal of this research is to present the theory of points for relatively cyclic and relatively relatively noncyclic p-contractions in complete locally

K

-convex spaces by providing basic conditions to ensure the existence and uniqueness of fixed points and best [...] Read more.

Our main goal of this research is to present the theory of points for relatively cyclic and relatively relatively noncyclic p-contractions in complete locally

K

-convex spaces by providing basic conditions to ensure the existence and uniqueness of fixed points and best proximity points of the relatively cyclic and relatively noncyclic p-contractions map in locally

K

-convex spaces. The result of this paper is the extension and generalization of the main results of Kirk and A. Abkar. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

13 pages, 256 KiB

Open AccessArticle

On Fixed Point Results for Modified JS-Contractions with Applications

by Vahid Parvaneh, Nawab Hussain, Aiman Mukheimer and Hassen Aydi

Axioms 2019, 8(3), 84; https://doi.org/10.3390/axioms8030084 - 24 Jul 2019

Cited by 14 | Viewed by 2701

Abstract

In [Fixed Point Theory Appl., 2015 (2015):185], the authors introduced a new concept of modified contractive mappings, generalizing Ćirić, Chatterjea, Kannan, and Reich type contractions. They applied the condition

(θ_{4})

(see page 3, ^{Section 2} of the above paper). Later, [...] Read more.

In [Fixed Point Theory Appl., 2015 (2015):185], the authors introduced a new concept of modified contractive mappings, generalizing Ćirić, Chatterjea, Kannan, and Reich type contractions. They applied the condition

(θ_{4})

(see page 3, ^{Section 2} of the above paper). Later, in [Fixed Point Theory Appl., 2016 (2016):62], Jiang et al. claimed that the results in [Fixed Point Theory Appl., 2015 (2015):185] are not real generalizations. In this paper, by restricting the conditions of the control functions, we obtain a real generalization of the Banach contraction principle (BCP). At the end, we introduce a weakly JS-contractive condition generalizing the JS-contractive condition. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

12 pages, 287 KiB

Open AccessArticle

Best Proximity Point Results for Geraghty Type Ƶ-Proximal Contractions with an Application

by Hüseyin Işık, Hassen Aydi, Nabil Mlaiki and Stojan Radenović

Axioms 2019, 8(3), 81; https://doi.org/10.3390/axioms8030081 - 18 Jul 2019

Cited by 6 | Viewed by 2999

Abstract

In this study, we establish the existence and uniqueness theorems of the best proximity points for Geraghty type Ƶ-proximal contractions defined on a complete metric space. The presented results improve and generalize some recent results in the literature. An example, as well as [...] Read more.

In this study, we establish the existence and uniqueness theorems of the best proximity points for Geraghty type Ƶ-proximal contractions defined on a complete metric space. The presented results improve and generalize some recent results in the literature. An example, as well as an application to a variational inequality problem are also given in order to illustrate the effectiveness of our generalizations. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

36 pages, 432 KiB

Open AccessArticle

Recent Advances on the Results for Nonunique Fixed in Various Spaces

by Erdal Karapınar

Axioms 2019, 8(2), 72; https://doi.org/10.3390/axioms8020072 - 05 Jun 2019

Cited by 9 | Viewed by 2707

Abstract

In this short survey, we aim to underline the importance of the non-unique fixed point results in various abstract spaces. We recall a brief background on the topic and we combine, collect and unify several existing non-unique fixed points in the literature. Some [...] Read more.

In this short survey, we aim to underline the importance of the non-unique fixed point results in various abstract spaces. We recall a brief background on the topic and we combine, collect and unify several existing non-unique fixed points in the literature. Some interesting examples are considered. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

9 pages, 264 KiB

Open AccessArticle

Fixed Point Theorems via α-ϱ-Fuzzy Contraction

by Badshah-e- Rome, Muhammad Sarwar and Poom Kumam

Axioms 2019, 8(2), 69; https://doi.org/10.3390/axioms8020069 - 31 May 2019

Cited by 1 | Viewed by 2786

Abstract

Some well known results from the existing literature are extended and generalized via new contractive type mappings in fuzzy metric spaces. A non trivial supporting example is also provided to demonstrate the validity of the obtained results. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

10 pages, 247 KiB

Open AccessArticle

Best Approximation Results in Various Frameworks

by Taoufik Sabar, Abdelhafid Bassou and Mohamed Aamri

Axioms 2019, 8(2), 67; https://doi.org/10.3390/axioms8020067 - 27 May 2019

Cited by 1 | Viewed by 2272

Abstract

We first provide a best proximity point result for quasi-noncyclic relatively nonexpansive mappings in the setting of dualistic partial metric spaces. Then, those spaces will be endowed with convexity and a result for a cyclic mapping will be obtained. Afterwards, we prove a [...] Read more.

We first provide a best proximity point result for quasi-noncyclic relatively nonexpansive mappings in the setting of dualistic partial metric spaces. Then, those spaces will be endowed with convexity and a result for a cyclic mapping will be obtained. Afterwards, we prove a best proximity point result for tricyclic mappings in the framework of the newly introduced extended partial

S_{b}

-metric spaces. In this way, we obtain extensions of some results in the literature. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

20 pages, 330 KiB

Open AccessArticle

Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application

by Atiya Perveen, Idrees A. Khan and Mohammad Imdad

Axioms 2019, 8(2), 49; https://doi.org/10.3390/axioms8020049 - 24 Apr 2019

Cited by 3 | Viewed by 2836

Abstract

In this paper, by introducing the concept of generalized Ćirić-type weak

(ϕ_{g}, R)

-contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation

R

. We also deduce some useful consequences showing the [...] Read more.

In this paper, by introducing the concept of generalized Ćirić-type weak

(ϕ_{g}, R)

-contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation

R

. We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

8 pages, 220 KiB

Open AccessArticle

Applications of Square Roots of Diffeomorphisms

by Yoshihiro Sugimoto

Axioms 2019, 8(2), 43; https://doi.org/10.3390/axioms8020043 - 11 Apr 2019

Viewed by 1949

Abstract

In this paper, we prove that on any contact manifold

(M, ξ)

there exists an arbitrary

C^{\infty}

-small contactomorphism which does not admit a square root. In particular, there exists an arbitrary

C^{\infty}

-small contactomorphism which is not [...] Read more.

In this paper, we prove that on any contact manifold

(M, ξ)

there exists an arbitrary

C^{\infty}

-small contactomorphism which does not admit a square root. In particular, there exists an arbitrary

C^{\infty}

-small contactomorphism which is not “autonomous”. This paper is the first step to study the topology of

C o n t_{0} (M, ξ) ∖ Aut (M, ξ)

. As an application, we also prove a similar result for the diffeomorphism group

Diff (M)

for any smooth manifold M. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

12 pages, 234 KiB

Open AccessArticle

Fixed Point Theorems for Geraghty Contraction Type Mappings in b-Metric Spaces and Applications

by Hamid Faraji, Dragana Savić and Stojan Radenović

Axioms 2019, 8(1), 34; https://doi.org/10.3390/axioms8010034 - 14 Mar 2019

Cited by 35 | Viewed by 3761

Abstract

In this paper, some new results are given on fixed and common fixed points of Geraghty type contractive mappings defined in b-complete b-metric spaces. Moreover, two examples are represented to show the compatibility of our results. Some applications for nonlinear integral [...] Read more.

In this paper, some new results are given on fixed and common fixed points of Geraghty type contractive mappings defined in b-complete b-metric spaces. Moreover, two examples are represented to show the compatibility of our results. Some applications for nonlinear integral equations are also given. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

13 pages, 652 KiB

Open AccessArticle

Best Proximity Point Theorems on Rectangular Metric Spaces Endowed with a Graph

by Nizar Souayah, Hassen Aydi, Thabet Abdeljawad and Nabil Mlaiki

Axioms 2019, 8(1), 17; https://doi.org/10.3390/axioms8010017 - 01 Feb 2019

Cited by 16 | Viewed by 3520

Abstract

In this paper, we ensure the existence and uniqueness of a best proximity point in rectangular metric spaces endowed with a graph structure. Full article

(This article belongs to the Special Issue Fixed Point Theory and Related Topics)

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