Iterative approximation of a common solution of split equilibrium, split variational inequality, and fixed point problem for a nonexpansive semigroup

2021 ◽  
Author(s):  
Shuja H. Rizvi ◽  
Fahad Sikander
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Fixed Point Problem ◽  
Nonexpansive Semigroup ◽  
Point Problem ◽  
Iterative Approximation ◽  
Common Solution ◽  
Split Variational Inequality

scholarly journals Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 187
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
General System ◽  
Inequality Constraint ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution ◽  
Common Fixed Point Problem ◽  
Monotone Variational Inequality

In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Strong convergence of the proposed method to the unique solution of the problem is established under some suitable assumptions.

scholarly journals Approximation results for split equilibrium problems and fixed point problems of nonexpansive semigroup in Hilbert spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yasir Arfat ◽  
Poom Kumam ◽  
Parinya Sa Ngiamsunthorn ◽  
Muhammad Aqeel Ahmad Khan ◽  
Hammad Sarwar ◽  
...  
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Nonexpansive Semigroup ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
Common Solution ◽  
Theoretical Results

Abstract In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and strong convergence characteristics of the proposed algorithm are investigated by employing suitable control conditions in such a setting of spaces. As a consequence, we provide a simplified analysis of various existing results concerning the extragradient method in the current literature. We also provide a numerical example to strengthen the theoretical results and the applicability of the proposed algorithm.

scholarly journals A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Francis Akutsah ◽  
Akindele Adebayo Mebawondu ◽  
Hammed Anuoluwapo Abass ◽  
Ojen Kumar Narain
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Hilbert Spaces ◽  
Lipschitz Constant ◽  
Adaptive Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Inertial Method ◽  
Split Variational Inequality ◽  
Monotone Variational Inequality

<p style='text-indent:20px;'>In this work, we propose a new inertial method for solving strongly monotone variational inequality problems over the solution set of a split variational inequality and composed fixed point problem in real Hilbert spaces. Our method uses stepsizes that are generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the operator norm as well as the Lipschitz constant of the operator. In addition, we prove that the proposed method converges strongly to a minimum-norm solution of the problem without using the conventional two cases approach. Furthermore, we present some numerical experiments to show the efficiency and applicability of our method in comparison with other methods in the literature. The results obtained in this paper extend, generalize and improve results in this direction.</p>

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