scholarly journals Retracted: On Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive-Like Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-1
Keyword(s):  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
The Common

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 On Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive-Like Operators

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
J. O. Olaleru ◽  
H. Akewe
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Weakly Compatible ◽  
The Common ◽  
Unique Common Fixed Point

We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations, and extensions of the work of Olatinwo and Imoru (2008), Olatinwo (2008). Consequently, several results in literature are generalized.

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 Modified Mixed Ishikawa Iteration for Common Fixed Points of Two Asymptotically Quasi Pseudocontractive Type Non-Self-Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yuanheng Wang ◽  
Huimin Shi
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Iterative Sequence ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Ishikawa Iterative Sequence

A new modified mixed Ishikawa iterative sequence with error for common fixed points of two asymptotically quasi pseudocontractive type non-self-mappings is introduced. By the flexible use of the iterative scheme and a new lemma, some strong convergence theorems are proved under suitable conditions. The results in this paper improve and generalize some existing results.

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 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 Fixed Points Approximation and Solutions of Some Equilibrium and Variational Inequalities Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Bashir Ali
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Strong Convergence Theorem ◽  
Points Approximation

We prove a new strong convergence theorem for an element in the intersection of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of some variational inequality problems, and the set of solutions of some equilibrium problems using a new iterative scheme. Our theorem generalizes and improves some recent results.

scholarly journals A Short Note on the Common Fixed Points of the Geraghty Contraction of Type ES,T

2018 ◽  
Vol 51 (1) ◽  
pp. 233-240 ◽  
Author(s):  
Badr Alqahtani ◽  
Andreea Fulga ◽  
Erdal Karapınar
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Necessary Conditions ◽  
Short Note ◽  
Common Fixed Points ◽  
Coincidence Points ◽  
The Common ◽  
Contraction Type

Abstract In this paper, we propose a new contraction type for two self-mappings and investigate the necessary conditions for the existence and uniqueness of coincidence points and common fixed points, respectively. We put some examples to illustrate our main results.

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