scholarly journals Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Hudson Akewe ◽  
Godwin Amechi Okeke ◽  
Adekunle F Olayiwola
Keyword(s):  
Strong Convergence ◽  
Iterative Schemes ◽  
Convergence And Stability ◽  
Contractive Type

scholarly journals Convergence and Stability of New Approximation Algorithms for Certain Contractive-Type Mappings

2021 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
Imo Kalu Agwu ◽  
Donatus Ikechi Igbokwe
Keyword(s):  
Approximation Algorithms ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Type Condition ◽  
Iterative Schemes ◽  
Convergence And Stability ◽  
Contractive Type ◽  
Stability Results

We present new fixed points algorithms called multistep H-iterative scheme and multistep SH-iterative scheme. Under certain contractive-type condition, convergence and stability results were established without any imposition of the ’sum conditions’, which to a large extent make some existing iterative schemes so far studied by other authors in this direction practically inefficient. Our results complement and improve some recent results in literature.

scholarly journals On Faster Implicit Hybrid Kirk-Multistep Schemes for Contractive-Type Operators

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
O. T. Wahab ◽  
K. Rauf
Keyword(s):  
Convergence Rate ◽  
Strong Convergence ◽  
Numerical Approach ◽  
Type Operator ◽  
Linear Spaces ◽  
Hybrid Schemes ◽  
Iterative Schemes ◽  
Normed Linear Spaces ◽  
Contractive Type ◽  
Stability Results

The purpose of this paper is to prove strong convergence and T-stability results of some modified hybrid Kirk-Multistep iterations for contractive-type operator in normed linear spaces. Our results show through analytical and numerical approach that the modified hybrid schemes are better in terms of convergence rate than other hybrid Kirk-Multistep iterative schemes in the literature.

scholarly journals Viscosity Approximation Methods for a Family of Nonexpansive Mappings in CAT(0) Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jinfang Tang
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Problem ◽  
Iterative Schemes ◽  
The Family ◽  
Viscosity Approximation Methods ◽  
Implicit And Explicit

The purpose of this paper is using the viscosity approximation method to study the strong convergence problem for a family of nonexpansive mappings in CAT(0) spaces. Under suitable conditions, some strong convergence theorems for the proposed implicit and explicit iterative schemes to converge to a common fixed point of the family of nonexpansive mappings are proved which is also a unique solution of some kind of variational inequalities. The results presented in this paper extend and improve the corresponding results of some others.

scholarly journals Convergence and stability of the three-step iterative schemes for a class of general quasivariational-like inequalities

2004 ◽  
Vol 2004 (70) ◽  
pp. 3849-3857
Author(s):  
Zeqing Liu ◽  
Zhefu An ◽  
Shin Min Kang ◽  
Jeong Sheok Ume
Keyword(s):  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Iterative Schemes ◽  
Convergence And Stability

We introduce and study a class of general quasivariational-like inequalities in Hilbert spaces, suggest two general algorithms, and establish the existence and uniqueness of solutions for these kinds of inequalities. Under certain conditions, we discuss convergence and stability of the three-step iterative sequences generated by the algorithms.

Modified CQ-Algorithms for G-Nonexpansive Mappings in Hilbert Spaces Involving Graphs

2020 ◽  
Vol 16 (01) ◽  
pp. 89-103
Author(s):  
W. Cholamjiak ◽  
D. Yambangwai ◽  
H. Dutta ◽  
H. A. Hammad
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Rate Of Convergence ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Iterative Schemes ◽  
Cq Method

In this paper, we introduce four new iterative schemes by modifying the CQ-method with Ishikawa and [Formula: see text]-iterations. The strong convergence theorems are given by the CQ-projection method with our modified iterations for obtaining a common fixed point of two [Formula: see text]-nonexpansive mappings in a Hilbert space with a directed graph. Finally, to compare the rate of convergence and support our main theorems, we give some numerical experiments.

scholarly journals On Rate of Convergence of Jungck-Type Iterative Schemes

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Nawab Hussain ◽  
Vivek Kumar ◽  
Marwan A. Kutbi
Keyword(s):  
Strong Convergence ◽  
Rate Of Convergence ◽  
Iterative Scheme ◽  
Convergence Speed ◽  
Contractive Condition ◽  
Iterative Schemes ◽  
The Stability

We introduce a new iterative scheme called Jungck-CR iterative scheme and study the stability and strong convergence of this iterative scheme for a pair of nonself-mappings using a certain contractive condition. Also, convergence speed comparison and applications of Jungck-type iterative schemes will be shown through examples.

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