scholarly journals Fixed Point Approximation for a Class of Generalized Nonexpansive Mappings in Hadamard Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Akbar Ali Khan ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Satisfying Condition ◽  
Iteration Process ◽  
Hadamard Space ◽  
Point Approximation ◽  
Convergence Results

In this paper, we establish strong and Δ convergence results for mappings satisfying condition B γ , μ through a newly introduced iterative process called JA iteration process. A nonlinear Hadamard space is used the ground space for establishing our main results. A novel example is provided for the support of our main results and claims. The presented results are the good extension of the corresponding results present in the literature.

AN ITERATIVE SCHEME FOR FIXED POINT PROBLEMS

2021 ◽  
Vol 10 (5) ◽  
pp. 2295-2316
Author(s):  
F. Akutsah ◽  
O. K. Narain ◽  
K. Afassinou ◽  
A. A. Mebawondu
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Satisfying Condition ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Examples ◽  
Convergence Results ◽  
The Stability

In this paper, we introduce a new three steps iteration process, prove that our newly proposed iterative scheme can be used to approximate the fixed point of a contractive-like mapping and establish some convergence results for our newly proposed iterative scheme generated by a mapping satisfying condition (E) in the framework of uniformly convex Banach space. In addition, with the aid of numerical examples, we established that our newly proposed iterative scheme is faster than the iterative process introduced by Ullah et al., [26], Karakaya et al., [16], Abass et. al. [1] and some existing iterative scheme in literature. More so, the stability of our newly proposed iterative process is presented and we also gave some numerical examples to display the efficiency of our proposed algorithm.

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 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 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.

scholarly journals Modified three step iterative process with errors for common fixed point of generalized asymptotically quasi-nonexpansive mappings

2012 ◽  
Vol 43 (4) ◽  
pp. 577-586
Author(s):  
Seyit Temir ◽  
Hükmi Kızıltunc
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Convergence Results ◽  
The Common

In this paper we introduce to modified three step iterative process with errors for approximating the common fixed point for generalized asymptotically quasi-nonexpansive mappings and prove some strong convergence results for the iterative sequences iterations with errors in real Banach spaces. The results obtained in this paper extend and improve the recent ones announced by Lan \cite{Lan}, Nantadilok \cite{Nan}, Saluja and Nashine \cite{SN} and Yang et all. \cite{LY} and many others.

scholarly journals A New Modified Fixed-Point Iteration Process

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3109
Author(s):  
Chanchal Garodia ◽  
Afrah A. N. Abdou ◽  
Izhar Uddin
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Weak Convergence ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
Fixed Point Iteration Process

In this paper, we present a new modified iteration process in the setting of uniformly convex Banach space. The newly obtained iteration process can be used to approximate a common fixed point of three nonexpansive mappings. We have obtained strong and weak convergence results for three nonexpansive mappings. Additionally, we have provided an example to support the theoretical proof. In the process, several relevant results are improved and generalized.

scholarly journals Convergence Results for a Common Solution of a Finite Family of Equilibrium Problems and Quasi-Bregman Nonexpansive Mappings in Banach Space

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
G. C. Ugwunnadi ◽  
Bashir Ali
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Equilibrium Problem ◽  
Iterative Process ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Common Solution ◽  
Convergence Results

We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem.

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.

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