scholarly journals Fixed points of monotone nonexpansive mappings on a hyperbolic metric space with a graph

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Monther Rashed Alfuraidan ◽  
Mohamed Amine Khamsi
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Nonexpansive Mappings ◽  
Hyperbolic Metric ◽  
Hyperbolic Metric Space

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.

COUNTING CONJUGACY CLASSES IN

2018 ◽  
Vol 97 (3) ◽  
pp. 412-421
Author(s):  
MICHAEL HULL ◽  
ILYA KAPOVICH
Keyword(s):  
Cayley Graph ◽  
Metric Space ◽  
Hyperbolic Metric ◽  
Conjugacy Classes ◽  
Finitely Generated ◽  
Finitely Generated Group ◽  
Irreducible Elements ◽  
Hyperbolic Metric Space

We show that if a finitely generated group$G$has a nonelementary WPD action on a hyperbolic metric space$X$, then the number of$G$-conjugacy classes of$X$-loxodromic elements of$G$coming from a ball of radius$R$in the Cayley graph of$G$grows exponentially in$R$. As an application we prove that for$N\geq 3$the number of distinct$\text{Out}(F_{N})$-conjugacy classes of fully irreducible elements$\unicode[STIX]{x1D719}$from an$R$-ball in the Cayley graph of$\text{Out}(F_{N})$with$\log \unicode[STIX]{x1D706}(\unicode[STIX]{x1D719})$of the order of$R$grows exponentially in$R$.

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 points of a finite family of I-asymptotically quasi-nonexpansive mappings in a convex metric space

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2175-2182 ◽  
Author(s):  
Birol Gündüz
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Metric Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Convex Metric Space ◽  
Convergence Theorems ◽  
Error Terms

In this paper, we study Ishikawa iterative scheme with error terms for a finite family of Iasymptotically quasi-nonexpansive mappings in a convex metric space. We established strong convergence theorems and their applications for the proposed algorithms in a convex metric space. Our theorems improve and extend the corresponding known results in Banach spaces.

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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