scholarly journals Strong Convergence Theorems by Modified Four Step Iterative Scheme with Errors for Three Nonexpansive Mappings

2015 ◽  
Vol 55 (3) ◽  
pp. 667-678
Author(s):  
PANKAJ KUMAR JHADE ◽  
AMARJEET SINGH SALUJA
Keyword(s):  
Strong Convergence ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convergence Theorems

Generalized three-step iteration schemes and common fixed points of three asymptotically quasi-nonexpansive mappings

2008 ◽  
Vol 41 (4) ◽  
Author(s):  
R. A. Rashwan ◽  
A. A. Abdel Hakim
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convergence Theorems

AbstractIn this paper, we study strong convergence theorems for a generalized three-step iterative scheme with errors to approximate common fixed points of three asymptotically quasi-nonexpansive mappings in real Banach spaces. Our results generalize and improve upon the corresponding results in [

scholarly journals Common fixed points of two finite families of nonexpansive mappings by iterations

2015 ◽  
Vol 31 (3) ◽  
pp. 325-331
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Uniformly Convex Banach Spaces

We study a Mann type iterative scheme for two finite families of nonexpansive mappings and establish 4− convergence and strong convergence theorems. The obtained results are applicable in uniformly convex Banach spaces (linear domain) and CAT (0) spaces (nonlinear domain) simultaneously.

scholarly journals Weak and strong convergence theorems for three Suzuki’s generalized nonexpansive mappings

2021 ◽  
Vol 110 (124) ◽  
pp. 121-129
Author(s):  
Seyit Temir
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems

We introduce a new iterative scheme for finding a common fixed point of three Suzuki?s generalized nonexpansive mappings in Banach spaces. We establish weak and strong convergence theorems for three Suzuki?s generalized nonexpansive mappings. The results obtained extend and improve the recent ones announced by Ali et al., Maniu and Thakur et al..

scholarly journals Fixed points of a finite family of I-asymptotically quasi-nonexpansive mappings in a convex metric space

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2175-2182 ◽  
Author(s):  
Birol Gündüz
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Metric Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Convex Metric Space ◽  
Convergence Theorems ◽  
Error Terms

In this paper, we study Ishikawa iterative scheme with error terms for a finite family of Iasymptotically quasi-nonexpansive mappings in a convex metric space. We established strong convergence theorems and their applications for the proposed algorithms in a convex metric space. Our theorems improve and extend the corresponding known results in Banach spaces.

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.

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