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.

scholarly journals Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Withun Phuengrattana ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Convex Metric Space ◽  
Convergence Theorems ◽  
Convex Metric Spaces

We introduce a new modified Halpern iteration for a countable infinite family of nonexpansive mappings{Tn}in convex metric spaces. We prove that the sequence{xn}generated by the proposed iteration is an approximating fixed point sequence of a nonexpansive mapping when{Tn}satisfies the AKTT-condition, and strong convergence theorems of the proposed iteration to a common fixed point of a countable infinite family of nonexpansive mappings in CAT(0) spaces are established under AKTT-condition and the SZ-condition. We also generalize the concept ofW-mapping for a countable infinite family of nonexpansive mappings from a Banach space setting to a convex metric space and give some properties concerning the common fixed point set of this family in convex metric spaces. Moreover, by using the concept ofW-mappings, we give an example of a sequence of nonexpansive mappings defined on a convex metric space which satisfies the AKTT-condition. Our results generalize and refine many known results in the current literature.

scholarly journals On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces

2021 ◽  
Vol 37 (3) ◽  
pp. 513-527
Author(s):  
JENJIRA PUIWONG ◽  
◽  
SATIT SAEJUNG ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Fixed Point Set ◽  
Convergence Theorems ◽  
Convex Metric Spaces ◽  
Strict Fixed Point ◽  
Point Set

We prove ∆-convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in p-uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the (CN) inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.

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 Fixed Point Results of a General Class of Monotone Nonexpansive Mappings in Hyperbolic Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Rida Outass ◽  
Karim Chaira ◽  
El Miloudi Marhrani ◽  
Nour-eddine El Harmouchi
Keyword(s):  
Fixed Point ◽  
General Class ◽  
Iterative Process ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Hyperbolic Metric ◽  
Ordered Metric Spaces ◽  
New Class

In this paper, we introduce and study some properties of a new class of generalized monotone nonexpansive mappings in hyperbolic metric spaces. Further, we give some results on the convergence of the Mann iterative process for this class of mappings in hyperbolic ordered metric spaces with some interesting examples.

scholarly journals Approximating Fixed Points of Reich–Suzuki Type Nonexpansive Mappings in Hyperbolic Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel De La Sen ◽  
Muhammad Naveed Khan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Iterative Process ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Hyperbolic Metric Space

In this work, we prove some strong and Δ convergence results for Reich-Suzuki type nonexpansive mappings through M iterative process. A uniformly convex hyperbolic metric space is used as underlying setting for our approach. We also provide an illustrate numerical example. Our results improve and extend some recently announced results of the metric fixed-point theory.

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 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].

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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