scholarly journals Convergence and stability of an iterative algorithm for strongly accretive Lipschitzian operator with applications

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3689-3704
Author(s):  
Vivek Kumar ◽  
Nawab Hussain ◽  
Abdul Khan ◽  
Faik Gürsoy
Keyword(s):  
Iterative Algorithm ◽  
Nonlinear Operator ◽  
Iterative Algorithms ◽  
Convergence Result ◽  
Nonlinear Operator Equation ◽  
Inclusion Problem ◽  
Convergence And Stability ◽  
Variational Inclusion Problem ◽  
Convergence Results ◽  
Stability Results

Using different technique and weaker restrictions on parameters, convergence and stability results of an SP iterative algorithm with errors for a strongly accretive Lipschitzian operator on a Banach space are established. Validity of new convergence results is verified through numerical examples and convergence comparison of various iterative algorithms is depicted. As applications of our convergence result, we solve a nonlinear operator equation and a variational inclusion problem. Our results are refinement and generalization of many classical results.

scholarly journals A new iterative algorithm for solving general variational inclusion problem with application

2021 ◽  
Author(s):  
M. Akram ◽  
A.F. Aljohani ◽  
M. Dilshad ◽  
Aysha Khan
Keyword(s):  
Differential Equation ◽  
Iterative Algorithm ◽  
Delay Differential Equation ◽  
Iterative Algorithms ◽  
Convergence Result ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Numerical Example ◽  
Variational Inclusion Problem ◽  
Delay Differential

In this paper, we pose a new iterative algorithm and show that this newly constructed algorithm converges faster than some existing iterative algorithms. We validate our claim by an illustrative example. Also, we discuss the convergence of our algorithm to approximate the solution of a general variational inclusion problem. Also, we present a numerical example to verify our existence and convergence result. Finally, we apply our proposed iterative algorithm to solve a delay differential equation as an application

scholarly journals Some Convergence and Stability Results for the Kirk Multistep and Kirk-SP Fixed Point Iterative Algorithms

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Faik Gürsoy ◽  
Vatan Karakaya ◽  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Iterative Algorithms ◽  
Iterative Processes ◽  
Convergence And Stability ◽  
The Stability ◽  
Stability Results

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related to the stability results for the Kirk multistep and Kirk-SP iterative processes by employing certain contractive-like operators. Our results generalize and unify some other results in the literature.

scholarly journals Convergence Analysis of a Three-Step Iterative Algorithm for Generalized Set-Valued Mixed-Ordered Variational Inclusion Problem

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 444
Author(s):  
Praveen. Agarwal ◽  
Doaa Filali ◽  
M. Akram ◽  
M. Dilshad
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Existence And Uniqueness Results ◽  
Variational Inclusion Problem ◽  
Uniqueness Results ◽  
Convergence Results ◽  
The Resolvent Operator

This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(·,·)-compression XOR-αM-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with H(·,·)-compression XOR-αM-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a ⊕ operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example.

scholarly journals The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 560 ◽  
Author(s):  
Pawicha Phairatchatniyom ◽  
Poom Kumam ◽  
Yeol Je Cho ◽  
Wachirapong Jirakitpuwapat ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Inclusion Problem ◽  
Common Elements ◽  
Inclusion Problems ◽  
Variational Inclusion Problem ◽  
Inertial Extrapolation ◽  
Appl Math

Based on the very recent work by Shehu and Agbebaku in Comput. Appl. Math. 2017, we introduce an extension of their iterative algorithm by combining it with inertial extrapolation for solving split inclusion problems and fixed point problems. Under suitable conditions, we prove that the proposed algorithm converges strongly to common elements of the solution set of the split inclusion problems and fixed point problems.

scholarly journals Generalized Implicit Set-Valued Variational Inclusion Problem with ⊕ Operation

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 421
Author(s):  
Rais Ahmad ◽  
Imran Ali ◽  
Saddam Husain ◽  
A. Latif ◽  
Ching-Feng Wen
Keyword(s):  
Resolvent Operator ◽  
Convergence Result ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Special Cases ◽  
The Resolvent Operator

In this paper, we consider a resolvent operator which depends on the composition of two mappings with ⊕ operation. We prove some of the properties of the resolvent operator, that is, that it is single-valued as well as Lipschitz-type-continuous. An existence and convergence result is proven for a generalized implicit set-valued variational inclusion problem with ⊕ operation. Some special cases of a generalized implicit set-valued variational inclusion problem with ⊕ operation are discussed. An example is constructed to illustrate some of the concepts used in this paper.

scholarly journals Projection Algorithms for Variational Inclusions

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Youli Yu ◽  
Pei-Xia Yang ◽  
Khalida Inayat Noor
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Real Hilbert Space ◽  
Projection Algorithm ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Variational Inclusions ◽  
Projection Algorithms ◽  
Variational Inclusion Problem

We present a projection algorithm for finding a solution of a variational inclusion problem in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a solution of the variational inclusion problem which also solves some variational inequality.

scholarly journals A ROBUST ITERATIVE APPROACH FOR SOLVING NONLINEAR VOLTERRA DELAY INTEGRO–DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 7 (2) ◽  
pp. 59
Author(s):  
Austine Efut Ofem ◽  
Unwana Effiong Udofia ◽  
Donatus Ikechi Igbokwe
Keyword(s):  
Differential Equations ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Stability Result ◽  
Iterative Approach ◽  
Weak And Strong Convergence ◽  
Mild Conditions ◽  
Convergence Results ◽  
The Stability

This paper presents a new iterative algorithm for approximating the fixed points of multivalued generalized \(\alpha\)–nonexpansive mappings. We study the stability result of our new iterative algorithm for a larger concept of stability known as weak \(w^2\)–stability. Weak and strong convergence results of the proposed iterative algorithm are also established. Furthermore, we show numerically that our new iterative algorithm outperforms several known iterative algorithms for multivalued generalized \(\alpha\)–nonexpansive mappings. Again, as an application, we use our proposed iterative algorithm to find the solution of nonlinear Volterra delay integro-differential equations. Finally, we provide an illustrative example to validate the mild conditions used in the result of the application part of this study. Our results improve, generalize and unify several results in the existing literature.

Iterative algorithms for split common fixed points of demicontractive operators without priori knowledge of operator norms

2018 ◽  
Vol 34 (3) ◽  
pp. 459-466
Author(s):  
YONGHONG YAO ◽  
◽  
JEN-CHIH YAO ◽  
YEONG-CHENG LIOU ◽  
MIHAI POSTOLACHE ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Convergence Result ◽  
Common Fixed Points ◽  
Operator Norms ◽  
Priori Knowledge

The split common fixed points problem for demicontractive operators has been studied in Hilbert spaces. An iterative algorithm is considered and the weak convergence result is given under some mild assumptions.

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