On variational inclusion and common fixed point problems in Hilbert spaces with applications

2010 ◽  
Vol 217 (7) ◽  
pp. 3000-3010 ◽  
Author(s):  
Yan Hao
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Variational Inclusion

scholarly journals Multistep hybrid viscosity method for split monotone variational inclusion and fixed point problems in Hilbert spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 5969-5992
Author(s):  
Jamilu Abubakar ◽  
◽  
Poom Kumam ◽  
Jitsupa Deepho ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Variational Inclusion ◽  
Viscosity Method

scholarly journals Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 844 ◽  
Author(s):  
Yaqin Wang ◽  
Xiaoli Fang ◽  
Tae-Hwa Kim
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
A Priori ◽  
Fixed Point Problems ◽  
A Priori Knowledge ◽  
Type Algorithm ◽  
Operator Norms ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point

We, first, propose a new method for solving split common fixed point problems for demicontractive mappings in Hilbert spaces, and then establish the strong convergence of such an algorithm, which extends the Halpern type algorithm studied by Wang and Xu to a viscosity iteration. Above all, the step sizes in this algorithm are chosen without a priori knowledge of the operator norms.

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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