Strong convergence results for variational inequalities and fixed point problems using modified viscosity implicit rules

2017 ◽  
Vol 77 (2) ◽  
pp. 535-558 ◽  
Author(s):  
Gang Cai ◽  
Yekini Shehu ◽  
Olaniyi Samuel Iyiola
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Point Problems ◽  
Convergence Results

scholarly journals Iterative Solutions for Solving Variational Inequalities and Fixed-Point Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Li-Jun Zhu ◽  
Naseer Shahzad ◽  
Asim Asiri
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Suggested Algorithm ◽  
Iterative Solutions

In this paper, we are interested in variational inequalities and fixed-point problems in Hilbert spaces. We present an iterative algorithm for finding a solution of the studied variational inequalities and fixed-point problems. We show the strong convergence of the suggested algorithm.

scholarly journals A strong convergence theorem for solving pseudo-monotone variational inequalities and fixed point problems using subgradient extragradient method in Banach spaces

2021 ◽  
Vol 7 (4) ◽  
pp. 5015-5028
Author(s):  
Fei Ma ◽  
◽  
Jun Yang ◽  
Min Yin
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Lipschitz Constant ◽  
Fixed Point Problems ◽  
Strong Convergence Theorem ◽  
Subgradient Extragradient Method ◽  
Step Size ◽  
Common Solution

<abstract><p>In this paper, we introduce an algorithm for solving variational inequalities problem with Lipschitz continuous and pseudomonotone mapping in Banach space. We modify the subgradient extragradient method with a new and simple iterative step size, and the strong convergence to a common solution of the variational inequalities and fixed point problems is established without the knowledge of the Lipschitz constant. Finally, a numerical experiment is given in support of our results.</p></abstract>

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