scholarly journals Approximation of Fixed Points of Multivalued Generalized (α,β)-Nonexpansive Mappings in an Ordered CAT(0) Space

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1945
Author(s):  
Mujahid Abbas ◽  
Hira Iqbal ◽  
Manuel De la De la Sen ◽  
Khushdil Ahmad
Keyword(s):  
Differential Equation ◽  
Fixed Points ◽  
Numerical Experiments ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Iteration Algorithm ◽  
Iterative Approximation ◽  
Convergence Results ◽  
Integral Differential Equation

The purpose of this article is to initiate the notion of monotone multivalued generalized (α,β)-nonexpansive mappings and explore the iterative approximation of the fixed points for the mapping in an ordered CAT(0) space. In particular, we employ the S-iteration algorithm in CAT(0) space to prove some convergence results. Moreover, some examples and useful results related to the proposed mapping are provided. Numerical experiments are also provided to illustrate and compare the convergence of the iteration scheme. Finally, an application of the iterative scheme has been presented in finding the solutions of integral differential equation.

scholarly journals Common Fixed Points of Multistep Noor Iterations with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
S. Imnang ◽  
S. Suantai
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Iteration Scheme ◽  
Finite Family ◽  
Special Cases

We introduce a general iteration scheme for a finite family of generalized asymptotically quasi-nonexpansive mappings in Banach spaces. The new iterative scheme includes the multistep Noor iterations with errors, modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor, and Khan and Takahashi scheme as special cases. Our results generalize and improve the recent ones announced by Khan et al. (2008), H. Fukhar-ud-din and S. H. Khan (2007), J. U. Jeong and S. H. Kim (2006), and many others.

scholarly journals Iterative approximations of common fixed points with simulation results in Banach spaces

2020 ◽  
Author(s):  
Ashis Bera ◽  
Ankush Chanda ◽  
Lakshmi Kanta Dey
Keyword(s):  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Iteration Scheme ◽  
The Other ◽  
The Novel ◽  
Weak And Strong Convergence ◽  
Analytic Proof ◽  
Convergence Results ◽  
The Common

In this article, we propose the Abbas-Nazir three step iteration scheme and employ the algorithm to study the common fixed points of a pair of generalized $\alpha$-Reich-Suzuki non-expansive mappings defined on a Banach space. Moreover, we explore a few weak and strong convergence results concerning such mappings. Our findings are aptly validated by non-trivial and constructive numerical examples and finally, we compare our results with that of the other noteworthy iterative schemes utilizing MATLAB $2017$a software. However, we perceive that for a different set of parameters and initial points, the newly proposed iterative scheme converges faster than the other well-known algorithms. To be specific, we give an analytic proof of the claim that the novel iteration scheme is also faster than that of Liu et al.

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.

A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces

2019 ◽  
Vol 28 (2) ◽  
pp. 191-198
Author(s):  
T. M. M. SOW
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Mann Iteration ◽  
Infinite Dimensional ◽  
Mann Algorithm

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results.

scholarly journals Convergence of Infinite Family of Multivalued Quasi-Nonexpansive Mappings Using Multistep Iterative Processes

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Renu Chugh ◽  
Sanjay Kumar
Keyword(s):  
Real Banach Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Finite Family ◽  
Countable Family ◽  
Uniformly Convex ◽  
Iterative Schemes ◽  
Strong And Weak Convergence ◽  
Convergence Results

We prove strong and weak convergence results using multistep iterative sequences for countable family of multivalued quasi-nonexpansive mappings by using some conditions in uniformly convex real Banach space. The results presented extended and improved the corresponding result of Zhang et al. (2013), Bunyawat and Suantai (2012), and some others from finite family, one countable family, and two countable families tok-number of countable families of multivalued quasi-nonexpansive mappings. Also we used a numerical example in C++ computational programs to prove that the iterative scheme we used has better rate of convergence than other existing iterative schemes.

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 Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1965-1971 ◽  
Author(s):  
Hafiz Fukhar-ud-din ◽  
Safeer Hussain Khan
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
The Common

A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.

scholarly journals Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme

2011 ◽  
Vol 24 (2) ◽  
pp. 97-102 ◽  
Author(s):  
Mujahid Abbas ◽  
Safeer Hussain Khan ◽  
Abdul Rahim Khan ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Points ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
One Step

scholarly journals Finding common fixed points of nonexpansive mappings by iteration

2000 ◽  
Vol 62 (2) ◽  
pp. 307-310 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Iteration Scheme ◽  
Finite Set

In this paper it is shown that a particular iteration scheme converges weakly to a common fixed point of a finite set of nonexpansive mappings. This result is an improvement of two related theorems in the literature.

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