scholarly journals Strong convergence inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Lipschitz Constant ◽  
Convergence Result ◽  
Common Element ◽  
Adaptive Technique ◽  
Prior Estimate ◽  
Adaptive Stepsize ◽  
Self Adaptive

AbstractIn this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseudocontractive mapping in real Hilbert spaces. The self-adaptive technique ensures the convergence of the algorithm without any prior estimate of the Lipschitz constant. With the aid of Moudafi’s viscosity approximation method, we prove a strong convergence result for the sequence generated by our algorithm under some mild conditions. We also provide some numerical examples to illustrate the accuracy and efficiency of the algorithm by comparing with other recent methods in the literature.

scholarly journals Extragradient methods with CQ technique for fixed point problems and equilibrium problems

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4783-4793
Author(s):  
Zhangsong Yao ◽  
Yeong-Cheng Liou ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Algorithms ◽  
Convergence Result ◽  
Fixed Point Problems ◽  
Common Element ◽  
Extragradient Methods ◽  
Extragradient Algorithm

In this paper, we study iterative algorithms for solving fixed point problems and equilibrium problems in Hilbert spaces. We present an extragradient algorithm with CQ technique for finding a common element of the fixed points of pseudocontractive operators and the solutions of pseudomonotone equilibrium problems. Strong convergence result of the proposed algorithm is proved.

scholarly journals A Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Pseudocontractive Mappings ◽  
Strict Pseudocontraction ◽  
Strictly Pseudocontractive Mappings

We prove a strong convergence theorem for a common fixed point of two sequences of strictly pseudocontractive mappings in Hilbert spaces. We also provide some applications of the main theorem to find a common element of the set of fixed points of a strict pseudocontraction and the set of solutions of an equilibrium problem in Hilbert spaces. The results extend and improve the recent ones announced by Marino and Xu (2007) and others.

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 General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Peichao Duan ◽  
Aihong Wang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings

We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of fixed point of infinitely many strict pseudocontractive mappings and the set of solutions of an equilibrium problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. Our results improve and extend the corresponding results reported by many others.

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 Generalized split null point of sum of monotone operators in Hilbert spaces

2021 ◽  
Vol 54 (1) ◽  
pp. 359-376
Author(s):  
Akindele A. Mebawondu ◽  
Hammed A. Abass ◽  
Olalwale K. Oyewole ◽  
Kazeem O. Aremu ◽  
Ojen K. Narain
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Monotone Operators ◽  
Convergence Result ◽  
Null Point ◽  
Iterative Technique ◽  
New Type ◽  
Inertial Extrapolation ◽  
Nonlinear Mappings

Abstract In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of GSMVI and fixed point problems of certain nonlinear mappings in the framework of real Hilbert spaces. Many existing results are derived as corollaries to our main result. Furthermore, we present a numerical example to support our main result and propose an open problem for interested researchers in this area. The result obtained in this paper improves and generalizes many existing results in the literature.

scholarly journals A Forward-Backward-Forward Algorithm for Solving Quasimonotone Variational Inequalities

2022 ◽  
Vol 2022 ◽  
pp. 1-8
Author(s):  
Tzu-Chien Yin ◽  
Nawab Hussain
Keyword(s):  
Variational Inequalities ◽  
Convergence Analysis ◽  
Prior Knowledge ◽  
Hilbert Spaces ◽  
Lipschitz Constant ◽  
Weak Continuity ◽  
Forward Algorithm ◽  
Adaptive Technique ◽  
Quasimonotone Operators ◽  
Self Adaptive

In this paper, we continue to investigate the convergence analysis of Tseng-type forward-backward-forward algorithms for solving quasimonotone variational inequalities in Hilbert spaces. We use a self-adaptive technique to update the step sizes without prior knowledge of the Lipschitz constant of quasimonotone operators. Furthermore, we weaken the sequential weak continuity of quasimonotone operators to a weaker condition. Under some mild assumptions, we prove that Tseng-type forward-backward-forward algorithm converges weakly to a solution of quasimonotone variational inequalities.

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 The Split Equality Fixed Point Problem of Demicontractive Operators with Numerical Example and Application

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 902
Author(s):  
Yaqin Wang ◽  
Jinzuo Chen ◽  
Ariana Pitea
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Numerical Example

This paper aims to propose a new reckoning method for solving the split equality fixed point problem of demicontractive operators in Hilbert spaces, and to establish a theorem with regard to the strong convergence of this new scheme. As an application, we also consider quasi-pseudo-contractive operators and obtain a result on the solution to the split equality fixed point problem in the framework of Hilbert spaces. A numerical example is also provided.

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