Abstract
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.
Highlights
The concept of inclusion problems and fixed point problems has been interesting to many mathematical researchers
A modified Tseng type algorithm is created based on the methods of Mann iterations and viscosity approximation
The purpose is to find a common solution to the inclusion problem of an L-Lipschitz continuous and monotone single-valued operator and a maximal monotone multivalued operator, and the fixed point problem of a nonexpansive operator
Summary
The concept of inclusion problems and fixed point problems has been interesting to many mathematical researchers. The step size rule for the problems was changed according to Mann and viscosity ideas This new method converges strongly under suitable assumptions and is convenient as a practical matter. There has been numerous research on the inclusion and fixed point problems. Zhang and Jiang [18] suggested a hybrid algorithm for the inclusion and fixed point problems for some operators. A very recent work of Cholamjiak, Kesornprom, and Pholasa [20] has been introduced to solve the inclusion problem of two monotone operators and the fixed point problems of nonexpansive mappings. This work suggests another algorithm to solve the inclusion and fixed point problems.
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