scholarly journals Fixed point results for nonexpansive mappings on metric spaces

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2011-2020
Author(s):  
Francesca Vetro
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Contraction Mappings

In this paper we obtain some fixed point results for a class of nonexpansive single-valued mappings and a class of nonexpansive multi-valued mappings in the setting of a metric space. The contraction mappings in Banach sense belong to the class of nonexpansive single-valued mappings considered herein. These results are generalizations of the analogous ones in Khojasteh et al. [Abstr. Appl. Anal. 2014 (2014), Article ID 325840].

scholarly journals Approximation of Endpoints for α—Reich–Suzuki Nonexpansive Mappings in Hyperbolic Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1692
Author(s):  
Izhar Uddin ◽  
Sajan Aggarwal ◽  
Afrah A. N. Abdou
Keyword(s):  
Fixed Point ◽  
Convergence Analysis ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Metric ◽  
Convergence Theorems ◽  
Hyperbolic Metric Space

The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving α—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and Δ—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results.

Fixed point theorems and convergence theorems for some monotone generalized nonexpansive mappings

2020 ◽  
Vol 36 (2) ◽  
pp. 199-204
Author(s):  
M. R. ALFURAIDAN ◽  
M. A. KHAMSI ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Coincidence Fixed Point

We present some new coincidence fixed point theorems for generalized multi-valued weak Γ-contraction mappings. Our outcomes extend several recent results in the framework of complete metric spaces endowed with a graph. Two illustrative examples are included and some consequences are derived.

scholarly journals New Generalizations of Set Valued Interpolative Hardy-Rogers Type Contractions in b-Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Muhammad Usman Ali ◽  
Hassen Aydi ◽  
Monairah Alansari
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Type Contraction

Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces and proved that on a complete b-metric space, whose all closed and bounded subsets are compact, the set valued interpolative Hardy-Rogers type contraction mapping has a fixed point. This article presents generalizations of above results by omitting the assumption that all closed and bounded subsets are compact.

scholarly journals On Multivalued Fuzzy Contractions in Extended b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Nayab Alamgir ◽  
Quanita Kiran ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Contraction Mappings ◽  
Nadler’S Fixed Point Theorem ◽  
The Family ◽  
Fuzzy Fixed Point

In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b -metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α -fuzzy fixed point theorems in the context of extended b -metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish α -fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.

scholarly journals Approximations of Fixed Points in the Hadamard Metric Space CATp(0)

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1088
Author(s):  
Mostafa Bachar ◽  
Mohamed Amine Khamsi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Approximate Fixed Point ◽  
Successive Iteration ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

In this paper, we consider the recently introduced C A T p ( 0 ) , where the comparison triangles belong to ℓ p , for p ≥ 2 . We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in C A T p ( 0 ) . Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence.

scholarly journals Some α − ϕ -Fuzzy Cone Contraction Results with Integral Type Application

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Saif Ur Rehman ◽  
Shamoona Jabeen ◽  
Sami Ullah Khan ◽  
Mohammed M. M. Jaradat
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Integral Type ◽  
Contraction Mappings ◽  
Theoretical Results ◽  
Cone Metric

In this paper, we define α -admissible and α - ϕ -fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our theoretical results have been utilized to show the existence of the solution to a nonlinear integral equation. This application is also illustrative of how fuzzy metric spaces can be used in other integral type operators.

scholarly journals Fixed Point Results for C -Contractive Mappings in Generalized Metric Spaces with a Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Karim Chaira ◽  
Mustapha Kabil ◽  
Abdessamad Kamouss
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Matrix Equations ◽  
Generalized Metric Spaces ◽  
Contraction Mappings ◽  
Contractive Mappings ◽  
Generalized Metric

In this paper, we establish fixed point theorems for Chatterjea contraction mappings on a generalized metric space endowed with a graph. Our results extend, generalize, and improve many of existing theorems in the literature. Moreover, some examples and an application to matrix equations are given to support our main result.

scholarly journals Fixed Point Results Using Ft-Contractions in Ordered Metric Spaces Having t-Property

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 313 ◽  
Author(s):  
Hassen Aydi ◽  
Tawseef Rashid ◽  
Qamrul Khan ◽  
Zead Mustafa ◽  
Mohammed Jaradat
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Contraction Mappings ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
New Concepts

In this paper, we prove the existence of fixed points of F t -contraction mappings in partially ordered metric spaces not necessarily complete. We require that the ordered metric space has the t-property, which is a new concept introduced recently by Rashid et.al. We also give some examples to illustrate the new concepts and obtained results.

scholarly journals A Study on Common Fixed Point of Joint A;B Generalized Cyclic ϕ−abc Weak Nonexpansive Mappings and Generalized Cyclic abc;r Contractions in Quasi Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Sahar Mohamed Ali Abou Bakr
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Convergence Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Compact Sets ◽  
Contraction Mappings

This manuscript proves the existence of a single common fixed point of two joint A,B generalized cyclic ϕ−abc weak nonexpansive mappings, where A and B are compact sets. The result in particular demonstrated a single fixed point of generalized cyclic ϕ−abc weak nonexpansive mappings, without the assumption of a single contracting point. Additionally, it introduces new types of generalized cyclic abc;r contraction mappings and describes the existence of a single fixed point of them in b-metric spaces. Finally, the presented results establish a simpler convergence theorem for a sequence of generalized cyclic abc;r contraction mappings, extend, and generalize some of the previous reported results.

scholarly journals On Generalized Rational α − Geraghty Contraction Mappings in G − Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
N. Priyobarta ◽  
Bulbul Khomdram ◽  
Yumnam Rohen ◽  
Naeem Saleem
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings

In this paper, we discuss about various generalizations of α − admissible mappings. Furthermore, we extend the concept of α − admissible to generalize rational α − Geraghty contraction in G − metric space. With this new contraction mapping, we establish some fixed-point theorems in G − metric space. The obtained result is verified with an example.

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