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.

scholarly journals Stability and Strong Convergence Results for Random Jungck-Kirk-Noor Iterative Scheme

2017 ◽  
Vol 58 (1) ◽  
pp. 167-182 ◽  
Author(s):  
R .A. Rashwan ◽  
H. A. Hammad
Keyword(s):  
Strong Convergence ◽  
Coincidence Point ◽  
Iterative Scheme ◽  
General Theorem ◽  
Stability And Convergence ◽  
Contractive Condition ◽  
Random Coincidence ◽  
Convergence Results ◽  
The Stability ◽  
Commuting Mappings

AbstractThe purpose of this study is to introduce a Jungck- Kirk-Noor type random iterative scheme and prove stability and strong convergence of this to establish a general theorem to approximate the unique common random coincidence point for two or more nonself random commuting mappings under general contractive condition in various spaces. Also we give the stability and convergence for random Jungck-Kirk-Ishikawa and random Jungck-Kirk-Mann as a corollaries. The results obtained in this paper improve the corresponding results announced recently.

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 A New Faster Iterative Scheme for Numerical Fixed Points Estimation of Suzuki’s Generalized Nonexpansive Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Shanza Hassan ◽  
Manuel De la Sen ◽  
Praveen Agarwal ◽  
Qasim Ali ◽  
Azhar Hussain
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces ◽  
The Stability

The purpose of this paper is to introduce a new four-step iteration scheme for approximation of fixed point of the nonexpansive mappings named as S∗-iteration scheme which is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our proposed scheme. We present a numerical example to show that our iteration scheme is faster than the aforementioned schemes. Moreover, we present some weak and strong convergence theorems for Suzuki’s generalized nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve, and unify many existing results in the literature.

scholarly journals A New Iterative Scheme for Approximation of Fixed Points of Suzuki's Generalized Nonexpansive Mappings

2021 ◽  
Author(s):  
Shivam Rawat ◽  
Ramesh Chandra Dimri ◽  
Ayush Bartwal
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces ◽  
The Stability

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

A study in the fixed point theory for a new iterative scheme and a class of generalized mappings

2018 ◽  
Vol 27 (2) ◽  
pp. 151-160
Author(s):  
KADRI DOGAN ◽  
◽  
VATAN KARAKAYA ◽  
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Rate Of Convergence ◽  
Iteration Method ◽  
Iterative Scheme ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Convergence Result ◽  
Iteration Scheme ◽  
Data Dependency

In this study, we introduce a new iteration scheme and prove the strong convergence result for this iteration method. We also compare the rate of convergence with the iterative scheme and the fixed point iteration scheme known as Picard-S due to Gursoy. Then we prove that this new iteration method is equivalent to convergence of the iteration schemes given in the introduction section of the manuscript. Moreover, we show the result of its data dependency.

scholarly journals Halpern–Ishikawa type iterative schemes for approximating fixed points of multi-valued non-self mappings

2020 ◽  
Author(s):  
Abebe R. Tufa ◽  
M. Thuto ◽  
M. Moetele
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Convergence Result ◽  
Nonempty Closed Convex Subset ◽  
Strictly Pseudocontractive Mapping ◽  
Iterative Schemes ◽  
Point Condition

Abstract Let C be a nonempty closed convex subset of a real Hilbert space H and $$T: C\rightarrow CB(H)$$ T : C → C B ( H ) be a multi-valued Lipschitz pseudocontractive nonself mapping. A Halpern–Ishikawa type iterative scheme is constructed and a strong convergence result of this scheme to a fixed point of T is proved under appropriate conditions. Moreover, an iterative method for approximating a fixed point of a k-strictly pseudocontractive mapping $$T: C\rightarrow Prox(H)$$ T : C → P r o x ( H ) is constructed and a strong convergence of the method is obtained without end point condition. The results obtained in this paper improve and extend known results in the literature.

scholarly journals Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xian Wang ◽  
Jun-min Chen ◽  
Hui Tong
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Scheme ◽  
Monotone Mapping ◽  
Generalized Resolvent ◽  
Iterative Schemes ◽  
Convergence Of The Scheme

We introduce a new generalized resolvent in a Banach space and discuss some of its properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.

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.

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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