scholarly journals Convergence and data dependence results of an iteration process in a hyperbolic space

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 569-582 ◽  
Author(s):  
Aynur Şahin ◽  
Metin Başarır
Keyword(s):  
Hyperbolic Space ◽  
Current Literature ◽  
Iteration Process ◽  
Data Dependence ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Appl Math ◽  
Dependence Result

In this paper we prove the strong and 4-convergence theorems of an iteration process of Khan et al. (J. Appl. Math. Comput. 35 (2011) 607-616) for three finite families of total asymptotically nonexpansive nonself mappings in a hyperbolic space. Moreover we obtain the data dependence result of this iteration for contractive-like mappings under some suitable conditions. Also we present some examples to support the results proved herein. Our results extend and improve some recent results announced in the current literature.

Some new results of M-iteration process in hyperbolic spaces

2019 ◽  
Vol 35 (2) ◽  
pp. 221-232
Author(s):  
AYNUR SAHIN ◽  
Keyword(s):  
Current Literature ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Data Dependence ◽  
Hyperbolic Spaces ◽  
Convergence Theorems ◽  
Contractive Type

In this paper, we study the M-iteration process in hyperbolic spaces and prove some strong and 4-convergence theorems of this iteration process for generalized nonexpansive mappings. Moreover, we establish the weak w2 - stability and data dependence theorems for a class of contractive-type mappings by using M-iteration process. The results presented here extend and improve some recent results announced in the current literature.

scholarly journals Convergence Theorems for Total Asymptotically Nonexpansive Mappings in Hyperbolic Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Liang-cai Zhao ◽  
Shih-sen Chang ◽  
Xiong Rui Wang
Keyword(s):  
Current Literature ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

The purpose of this paper is to introduce the concept oftotal asymptotically nonexpansive mappingsand to prove someΔ-convergence theorems of the iteration process for this kind of mappings in the setting ofhyperbolic spaces. The results presented in the paper extend and improve some recent results announced in the current literature.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

scholarly journals -Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Luo Yi Shi ◽  
Ru Dong Chen ◽  
Yu Jing Wu
Keyword(s):  
Fixed Point ◽  
Convex Subset ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Convergence Problems

New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self-mapping of a closed convex subset of a CAT(0) space . Consider the iteration process , where is arbitrary and or for , where . It is shown that under certain appropriate conditions on   △-converges to a fixed point of .

scholarly journals Three-step iterations for total asymptotically nonexpansive mappings in CAT(0) spaces

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1317-1330 ◽  
Author(s):  
Gurucharan Saluja ◽  
Mihai Postolache
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Convergence Theorems ◽  
Demiclosed Principle ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings ◽  
Appl Math

In this paper, we establish strong and ?-convergence theorems of modified three-step iterations for total asymptotically nonexpansive mapping which is wider than the class asymptotically nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and generalize the corresponding results of Chang et al. [Demiclosed principle and ?-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Appl. Math. Comput. 219(5) (2012) 2611-2617], Nanjaras and Panyanak [Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. Vol. 2010, Art. ID 268780], and many others.

scholarly journals Convergence Rate of Implicit Iteration Process and a Data Dependence Result

2018 ◽  
Vol 11 (1) ◽  
pp. 189
Author(s):  
Isa Yildirim ◽  
Mujahid Abbas
Keyword(s):  
Convergence Rate ◽  
Rate Of Convergence ◽  
Iteration Process ◽  
Data Dependence ◽  
Hyperbolic Spaces ◽  
Type Mapping ◽  
Contractive Type ◽  
Iteration Processes ◽  
Implicit Iteration ◽  
Dependence Result

The aim of this paper is to introduce an implicit S-iteration processand study its convergence in the framework of W-hyperbolic spaces. We showthat the implicit S-iteration process has higher rate of convergence than implicit Mann type iteration and implicit Ishikawa-type iteration processes. We present a numerical example to support the analytic result proved herein. Finally, we prove a data dependence result for a contractive type mapping using implicit S-iteration process.

scholarly journals Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Murat Ozdemir ◽  
Sezgin Akbulut ◽  
Hukmi Kiziltunc
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Scheme ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive

We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003), Wang (2006), Shahzad (2005), and Thianwan (2008).

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