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.

scholarly journals Approximating Stationary Points of Multivalued Generalized Nonexpansive Mappings in Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Muhammad Arshad ◽  
Manuel de la Sen ◽  
Muhammad Safi Ullah Khan
Keyword(s):  
Current Literature ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Stationary Points ◽  
Uniformly Convex ◽  
Numerical Example

In this research, under some appropriate conditions, we approximate stationary points of multivalued Suzuki mappings through the modified Agarwal-O’Regan-Sahu iteration process in the setting of 2-uniformly convex hyperbolic spaces. We also provide an illustrative numerical example. Our results improve and extend some recently announced results of the current literature.

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 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.

scholarly journals Convergence theorems for a family of multivalued nonexpansive mappings in hyperbolic spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 1065-1073 ◽  
Author(s):  
Osman Alagoz ◽  
Birol Gunduz ◽  
Sezgin Akbulut
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Hyperbolic Spaces ◽  
Multivalued Mappings ◽  
Convergence Theorems

AbstractIn this article we modify an iteration process to prove strong convergence and Δ— convergence theorems for a finite family of nonexpansive multivalued mappings in hyperbolic spaces. The results presented here extend some existing results in the literature.

Some convergence results for nonexpansive mappings in uniformly convex hyperbolic spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 331-338
Author(s):  
AYNUR SAHIN ◽  
◽  
METIN BASARIR ◽  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Convergence Results ◽  
Uniformly Convex Hyperbolic Space

In this paper, we establish some strong and 4-convergence theorems of an iteration process for approximating a common fixed point of three nonexpansive mappings in a uniformly convex hyperbolic space. The results presented here extend and improve various results in the existing literature.

scholarly journals Fixed Point Approximation of Generalized Nonexpansive Mappings in Hyperbolic Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Jong Kyu Kim ◽  
Ramesh Prasad Pathak ◽  
Samir Dashputre ◽  
Shailesh Dhar Diwan ◽  
Rajlaxmi Gupta
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Point Approximation

We prove strong and Δ-convergence theorems for generalized nonexpansive mappings in uniformly convex hyperbolic spaces using S-iteration process due to Agarwal et al. As uniformly convex hyperbolic spaces contain Banach spaces as well as CAT(0) spaces, our results can be viewed as extension and generalization of several well-known results in Banach spaces as well as CAT(0) spaces.

scholarly journals Fixed-Point Approximations of Generalized Nonexpansive Mappings via Generalized M-Iteration Process in Hyperbolic Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Hyperbolic Spaces ◽  
Convergence Theorems ◽  
Numerical Example

In this paper, we propose the generalized M-iteration process for approximating the fixed points from Banach spaces to hyperbolic spaces. Using our new iteration process, we prove Δ-convergence and strong convergence theorems for the class of mappings satisfying the condition Cλ and the condition E which is the generalization of Suzuki generalized nonexpansive mappings in the setting of hyperbolic spaces. Moreover, a numerical example is given to present the capability of our iteration process and the solution of the integral equation is also illustrated using our main result.

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