scholarly journals Tseng Type Methods for Inclusion and Fixed Point Problems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1175 ◽  
Author(s):  
Raweerote Suparatulatorn ◽  
Anchalee Khemphet
Keyword(s):  
Fixed Point ◽  
Numerical Experiments ◽  
Fixed Point Problems ◽  
Feasibility Problem ◽  
Signal Recovery ◽  
Viscosity Approximation ◽  
Inclusion Problems ◽  
Convex Feasibility ◽  
Previous Algorithm ◽  
Viscosity Approximation Methods

An algorithm is introduced to find an answer to both inclusion problems and fixed point problems. This algorithm is a modification of Tseng type methods inspired by Mann’s type iteration and viscosity approximation methods. On certain conditions, the iteration obtained from the algorithm converges strongly. Moreover, applications to the convex feasibility problem and the signal recovery in compressed sensing are considered. Especially, some numerical experiments of the algorithm are demonstrated. These results are compared to those of the previous algorithm.

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.

scholarly journals Hierarchical Fixed Point Problems in Uniformly Smooth Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen ◽  
Chin-Tzong Pang
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Problems ◽  
Approximation Methods ◽  
Viscosity Approximation ◽  
Uniformly Smooth ◽  
Hierarchical Fixed Point ◽  
Viscosity Approximation Methods ◽  
Uniformly Smooth Banach Spaces ◽  
Hierarchical Fixed Point Problems

We propose some relaxed implicit and explicit viscosity approximation methods for hierarchical fixed point problems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These relaxed viscosity approximation methods are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under mild conditions.

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