scholarly journals A New Iterative Scheme for Solving the Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Pakkapon Preechasilp
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Common Solution

We introduce the new iterative methods for finding a common solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space. The main result extends various results existing in the current literature.

scholarly journals Strong Convergence Theorems for Equilibrium Problems andk-Strict Pseudocontractions in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dao-Jun Wen
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Finite Family ◽  
Common Element ◽  
Convergence Theorems

We introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed point of a finite family ofk-strictly pseudo-contractive nonself-mappings. Strong convergence theorems are established in a real Hilbert space under some suitable conditions. Our theorems presented in this paper improve and extend the corresponding results announced by many others.

scholarly journals Convergence Theorems of Iterative Schemes For Nonexpansive Mappings

2017 ◽  
Vol 12 (12) ◽  
pp. 6845-6851
Author(s):  
Inaam Mohammed Ali Hadi ◽  
Dr. salwa Salman Abd
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Common Fixed Point ◽  
Convex Analysis ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Iterative Schemes

In this paper, we give a type of iterative scheme for sequence of nonexpansive mappings and we study the strongly convergence of these schemes in real Hilbert space to common fixed point which is also a solution of a variational inequality. Also there are some consequent of this results in convex analysis

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals Approximation of Common Fixed Points of a Sequence of Nearly Nonexpansive Mappings and Solutions of Variational Inequality Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
D. R. Sahu ◽  
Shin Min Kang ◽  
Vidya Sagar
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Variational Inequality Problem ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Strong Convergence Theorem

We introduce an explicit iterative scheme for computing a common fixed point of a sequence of nearly nonexpansive mappings defined on a closed convex subset of a real Hilbert space which is also a solution of a variational inequality problem. We prove a strong convergence theorem for a sequence generated by the considered iterative scheme under suitable conditions. Our strong convergence theorem extends and improves several corresponding results in the context of nearly nonexpansive mappings.

scholarly journals An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Mohammad Farid ◽  
Rehan Ali
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Fixed Point Problems ◽  
Variational Inclusion ◽  
Common Solution ◽  
New Type

Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established theorem. Finally, we provide a numerical example to demonstrate the applicability of the algorithm. We emphasize that the result accounted in manuscript unifies and extends various results in this field of study.

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 Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 480
Author(s):  
Manatchanok Khonchaliew ◽  
Ali Farajzadeh ◽  
Narin Petrot
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Numerical Experiments ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
Constraint Qualifications ◽  
Solution Sets ◽  
New Algorithms

This paper presents two shrinking extragradient algorithms that can both find the solution sets of equilibrium problems for pseudomonotone bifunctions and find the sets of fixed points of quasi-nonexpansive mappings in a real Hilbert space. Under some constraint qualifications of the scalar sequences, these two new algorithms show strong convergence. Some numerical experiments are presented to demonstrate the new algorithms. Finally, the two introduced algorithms are compared with a standard, well-known algorithm.

scholarly journals Parallel and Cyclic Algorithms for Quasi-Nonexpansives in Hilbert Space

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Bin-Chao Deng ◽  
Tong Chen ◽  
Baogui Xin
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings

Let{T}i=1NbeNquasi-nonexpansive mappings defined on a closed convex subsetCof a real Hilbert spaceH. Consider the problem of finding a common fixed point of these mappings and introduce the parallel and cyclic algorithms for solving this problem. We will prove the strong convergence of these algorithms.

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.

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