Analysis of two variants of an inertial projection algorithm for finding the minimum-norm solutions of variational inequality and fixed point problems

2021 ◽  
Author(s):  
Ha Manh Linh ◽  
Simeon Reich ◽  
Duong Viet Thong ◽  
Vu Tien Dung ◽  
Nguyen Phuong Lan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Fixed Point Problems ◽  
Projection Algorithm ◽  
Minimum Norm

scholarly journals Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 236 ◽  
Author(s):  
Bing Tan ◽  
Shanshan Xu ◽  
Songxiao Li
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Location Theory ◽  
Fixed Point Problems ◽  
Projection Algorithm ◽  
Feasibility Problem ◽  
Projection Algorithms ◽  
Convex Feasibility ◽  
Mann Algorithm

In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.

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