In this paper, we consider a type of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces that are the sum of monotone operators and fixed point problems. By assuming the existence of solutions, we provide a suitable algorithm for finding a solution point. Some important applications and numerical experiments of the considered problem and constructed algorithm are also discussed.MSC: 26A18; 47H04; 47H05; 47H10; 54A20
In this paper, we consider the split monotone variational inclusion problem in Hilbert spaces. By assuming the existence of solutions, we introduce an iterative algorithm, in which the stepsizes does not need any prior information about the operator norm, and show its convergence theorem. Some applications and numerical experiments of the considered problem are also discussed.Keywords: Split monotone variational inclusion problem, maximal monotone operator, inverse strongly monotone operator, convergence theorems.
We consider the split feasibility problem in Hilbert spaces when the hard constraint is common solutions of zeros of the sum of monotone operators and fixed point sets of a finite family of nonexpansive mappings, while the soft constraint is the inverse image of a fixed point set of a nonexpansive mapping. We introduce iterative algorithms for the weak and strong convergence theorems of the constructed sequences. Some numerical experiments of the introduced algorithm are also discussed.
In this paper, we present two iterative algorithms for approximating a solution of the split feasibility problem on zeros of a sum of monotone operators and fixed points of a finite family of nonexpansive mappings. Weak and strong convergence theorems are proved in the framework of Hilbert spaces under some mild conditions. We apply the obtained main result for the problem of finding a common zero of the sum of inverse strongly monotone operators and maximal monotone operators, for finding a common zero of a finite family of maximal monotone operators, for finding a solution of multiple sets split common null point problem, and for finding a solution of multiple sets split convex feasibility problem. Some applications of the main results are also provided.
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