A STRONGLY CONVERGENT SHRINKING DESCENT-LIKE HALPERN’S METHOD FOR MONOTONE VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS

2014 ◽  
Vol 39 (3) ◽  
pp. 379-391
Author(s):  
Nguyen Thi Thu Thuy
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Fixed Point Problems ◽  
Monotone 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.

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