scholarly journals Iterative Scheme for Split Variational Inclusion and a Fixed-Point Problem of a Finite Collection of Nonexpansive Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
M. Dilshad ◽  
A. F. Aljohani ◽  
M. Akram
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Common Element ◽  
Finite Collection ◽  
Point Problem ◽  
Common Solution ◽  
The Common

This article is aimed at introducing an iterative scheme to approximate the common solution of split variational inclusion and a fixed-point problem of a finite collection of nonexpansive mappings. It is proven that under some suitable assumptions, the sequences achieved by the proposed iterative scheme converge strongly to a common element of the solution sets of these problems. Some consequences of the main theorem are also given. Finally, the convergence analysis of the sequences achieved from the iterative scheme is illustrated with the help of a numerical example.

scholarly journals Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Gendai Gu ◽  
Shenghua Wang ◽  
Yeol Je Cho
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequalities ◽  
Common Fixed Point ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Hierarchical Fixed Point ◽  
The Common

We introduce a new iterative scheme that converges strongly to a common fixed point of a countable family of nonexpansive mappings in a Hilbert space such that the common fixed point is a solution of a hierarchical fixed point problem. Our results extend the ones of Moudafi, Xu, Cianciaruso et al., and Yao et al.

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

scholarly journals Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Fixed Point Set ◽  
Common Fixed Point Problem ◽  
The Family ◽  
Point Set ◽  
The Common

It is our purpose in this paper to prove two convergents of viscosity approximation scheme to a common fixed point of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, it is the unique solution in to a certain variational inequality, where stands for the common fixed-point set of the family of multivalued nonexpansive mapping .

scholarly journals Strong convergence algorithm for the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem

2021 ◽  
pp. 1-32
Author(s):  
Shamshad Husain ◽  
Mohd Asad ◽  
Mubashshir Uddin Khairoowala
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Common Element ◽  
Point Problem ◽  
Variational Inclusions ◽  
Generalized Equilibrium Problem ◽  
Solution Sets ◽  
Generalized Equilibrium ◽  
Split Generalized Equilibrium Problem

The purpose of this paper is to recommend an iterative scheme to approximate a common element of the solution sets of the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem for non-expansive mappings. We prove that the sequences generated by the recommended iterative scheme strongly converge to a common element of solution sets of stated split problems. In the end, we provide a numerical example to support and justify our main result. The result studied in this paper generalizes and extends some widely recognized results in this direction.

scholarly journals A Common Solution of Equilibrium, Constrained Convex Minimization, and Fixed Point Problems

2021 ◽  
Vol 52 ◽  
Author(s):  
Maryam Yazdi
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Convex Minimization ◽  
Projection Algorithm ◽  
Point Problem ◽  
Constrained Convex Minimization ◽  
Common Solution ◽  
Numerical Result ◽  
Constrained Convex Minimization Problem

In this paper, we propose a new iterative scheme with the help of the gradient- projection algorithm (GPA) for finding a common solution of an equilibrium problem, a constrained convex minimization problem, and a fixed point problem. Then, we prove some strong convergence theorems which improve and extend some recent results. Moreover, we give a numerical result to show the validity of our main theorem.

A viscosity-type proximal point algorithm for monotone equilibrium problem and fixed point problem in an Hadamard space

2020 ◽  
pp. 2150058
Author(s):  
K. O. Aremu ◽  
C. Izuchukwu ◽  
A. A. Mebawondu ◽  
O. T. Mewomo
Keyword(s):  
Fixed Point ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Feasibility Problem ◽  
Point Problem ◽  
Hadamard Space ◽  
Proximal Point ◽  
Common Solution

In this paper, we introduce a viscosity-type proximal point algorithm comprising of a finite composition of resolvents of monotone bifunctions and a generalized asymptotically nonspreading mapping recently introduced by Phuengrattana [Appl. Gen. Topol. 18 (2017) 117–129]. We establish a strong convergence result of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a generalized asymptotically nonspreading and nonexpansive mappings, which is also a unique solution of some variational inequality problems in an Hadamard space. We apply our result to solve convex feasibility problem and to approximate a common solution of a finite family of minimization problems in an Hadamard space.

scholarly journals Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 255
Author(s):  
Yan Tang ◽  
Yeol Cho
Keyword(s):  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Common Element ◽  
Inclusion Problem ◽  
Point Problem ◽  
Step Size ◽  
Convergence Theorems ◽  
Common Solution ◽  
Variational Inclusion Problem

In this paper, the split variational inclusion problem (SVIP) and the system of equilibrium problems (EP) are considered in Hilbert spaces. Inspired by the works of Byrne et al., López et al., Moudafi and Thukur, Sobumt and Plubtieng, Sitthithakerngkiet et al. and Eslamian and Fakhri, a new self-adaptive step size algorithm is proposed to find a common element of the solution set of the problems SVIP and EP. Convergence theorems are established under suitable conditions for the algorithm and application to the common solution of the fixed point problem, and the split convex optimization problem is considered. Finally, the performances and computational experiments are presented and a comparison with the related algorithms is provided to illustrate the efficiency and applicability of our new algorithms.

scholarly journals A new viscosity-type iteration for a finite family of split variational inclusion and fixed point problems between Hilbert and Banach spaces

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
C. Izuchukwu ◽  
F. O. Isiogugu ◽  
C. C. Okeke
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Iteration Process ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Point Problem ◽  
Common Solution

Abstract In this paper, we introduce a new viscosity-type iteration process for approximating a common solution of a finite family of split variational inclusion problem and fixed point problem. We prove that the proposed algorithm converges strongly to a common solution of a finite family of split variational inclusion problems and fixed point problem for a finite family of type-one demicontractive mappings between a Hilbert space and a Banach space. Furthermore, we applied our results to study a finite family of split convex minimization problems, and also considered a numerical experiment of our results to further illustrate its applicability. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13:759–775, 2012), Kazmi and Rizvi (Optim. Lett. 8(3):1113–1124, 2014), Moudafi (J. Optim. Theory Appl. 150:275–283, 2011), Shehu and Ogbuisi (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 110(2):503–518, 2016), Takahashi and Yao (Fixed Point Theory Appl. 2015:87, 2015), Chidume and Ezeora (Fixed Point Theory Appl. 2014:111, 2014), and a host of other important results in this direction.

scholarly journals Strong convergence for monotone bilevel equilibria with constraints of variational inequalities and fixed points using subgradient extragradient implicit rule

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Long He ◽  
Yun-Ling Cui ◽  
Lu-Chuan Ceng ◽  
Tu-Yan Zhao ◽  
Dan-Qiong Wang ◽  
...  
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution ◽  
Implicit Rule

AbstractIn a real Hilbert space, let GSVI and CFPP represent a general system of variational inequalities and a common fixed point problem of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping, respectively. In this paper, via a new subgradient extragradient implicit rule, we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP constraints, i.e., a strongly monotone equilibrium problem over the common solution set of another monotone equilibrium problem, the GSVI and the CFPP. Some strong convergence results for the proposed algorithms are established under the mild assumptions, and they are also applied for finding a common solution of the GSVI, VIP, and FPP, where the VIP and FPP stand for a variational inequality problem and a fixed point problem, respectively.

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