The modified viscosity implicit rules for variational inequality problems and fixed point problems of nonexpansive mappings in Hilbert spaces

2019 ◽  
Vol 113 (4) ◽  
pp. 3545-3562 ◽  
Author(s):  
Gang Cai ◽  
Yekini Shehu ◽  
Olaniyi Samuel Iyiola
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Variational Inequality Problems ◽  
Fixed Point Problems

scholarly journals An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Mohammad Farid ◽  
Rehan Ali
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Fixed Point Problems ◽  
Variational Inclusion ◽  
Common Solution ◽  
New Type

Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established theorem. Finally, we provide a numerical example to demonstrate the applicability of the algorithm. We emphasize that the result accounted in manuscript unifies and extends various results in this field of study.

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