Viscosity interative algorithms with errors for two nonexpansive mappings and variational inequalities

2015 ◽  
pp. 289-294 ◽  
Keyword(s):  
Variational Inequalities ◽  
Nonexpansive Mappings

scholarly journals Viscosity explicit midpoint methods for nonexpansive mappings in Hadamard spaces

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1347-1357
Author(s):  
Pakkapon Preechasilp
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Equilibrium Problem ◽  
Nonexpansive Mappings ◽  
Midpoint Method ◽  
Approximating Sequence

In this paper, the viscosity explicit midpoint method for nonexpansive mappings in Hadamard spaces is introduced. Under certain appropriate conditions on the sequence of parameters, it is proved that the limit of the approximating sequence generated by proposed method converges strongly to a fixed point of T which solves some variational inequalities. Moreover, we give an application to the equilibrium problem.

scholarly journals Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 218
Author(s):  
Lu-Chuan Ceng ◽  
Xiaoye Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mappings ◽  
General System ◽  
Inequality Constraint ◽  
Common Solution ◽  
Iteration Methods ◽  
Monotone Variational Inequality ◽  
Implicit Iteration

This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions.

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