scholarly journals Some fixed points properties, strong and ∆-convergence results for generalized α-nonexpansive mappings in hyperbolic spaces

2018 ◽  
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Convergence Results

Iteration schema for common fixed points of nonlinear mappings in spaces of nonpositive curvature

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Muhammad Aqeel Ahmad Khan
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Nonpositive Curvature ◽  
Common Fixed Points ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
One Step ◽  
Uniformly Continuous ◽  
Nonlinear Mappings

Abstract.In this paper, we propose a one-step iteration for the approximation of common fixed points of two uniformly continuous total asymptotically quasi-nonexpansive mappings in uniformly convex hyperbolic spaces. We establish strong convergence and Δ-convergence results of the proposed iteration in this setting. As a consequence, our convergence results improve and generalize various results announced in the current literature.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Amna Kalsoom ◽  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Tareq M. Al-Shami ◽  
Amna Bibi ◽  
...  
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Hyperbolic Space ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Point Approximation ◽  
Convergence Results ◽  
Iteration Processes

Fixed points of monotone α -nonexpansive and generalized β -nonexpansive mappings have been approximated in Banach space. Our purpose is to approximate the fixed points for the above mappings in hyperbolic space. We prove the existence and convergence results using some iteration processes.

Some convergence results of M iterative process in Banach spaces

2019 ◽  
pp. 2150017 ◽  
Author(s):  
Kifayat Ullah ◽  
Faiza Ayaz ◽  
Junaid Ahmad
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Weak And Strong Convergence ◽  
Convergence Results

In this paper, we prove some weak and strong convergence results for generalized [Formula: see text]-nonexpansive mappings using [Formula: see text] iteration process in the framework of Banach spaces. This generalizes former results proved by Ullah and Arshad [Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process, Filomat 32(1) (2018) 187–196].

scholarly journals Some Convergence Results for a Class of Generalized Nonexpansive Mappings in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel de la Sen ◽  
Muhammad Naveed Khan
Keyword(s):  
Weak Convergence ◽  
Iterative Method ◽  
Fixed Points ◽  
Banach Spaces ◽  
Current Literature ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces

This paper investigates fixed points of Reich-Suzuki-type nonexpansive mappings in the context of uniformly convex Banach spaces through an M ∗ iterative method. Under some appropriate situations, some strong and weak convergence theorems are established. To support our results, a new example of Reich-Suzuki-type nonexpansive mappings is presented which exceeds the class of Suzuki-type nonexpansive mappings. The presented results extend some recently announced results of current literature.

scholarly journals Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Hyperbolic Space ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
Uniformly Convex Hyperbolic Space

We use a three-step iterative process to prove some strong andΔ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.

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 Common Fixed Points of Two Multivalued Asymptotically Nonexpansive Mappings

2019 ◽  
Vol 12 (2) ◽  
pp. 348-357
Author(s):  
Safeer Hussain Khan ◽  
Hira Iqbal ◽  
Mujahid Abbas
Keyword(s):  
Fixed Points ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Ishikawa Iterative Process

In this paper, we construct a modified Ishikawa iterative process to approximate common fixed points for two multivalued asymptotically nonexpansive mappings and prove some convergence theorems in uniformly convex hyperbolic spaces.

scholarly journals A new iteration scheme for approximating fixed points of nonexpansive mappings

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2711-2720 ◽  
Author(s):  
Balwant Thakur ◽  
Dipti Thakur ◽  
Mihai Postolache
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Iteration Scheme ◽  
Numerical Example ◽  
Convergence Results ◽  
Iteration Processes

In this paper, we introduce a new three-step iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that the new iteration process is faster than a number of existing iteration processes. To support the claim, we consider a numerical example and approximated the fixed point numerically by computer using MATLAB.

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