Abstract
In this paper, a monotone inclusion problem and a fixed point problem of nonexpansive mappings are investigated based on a Mann-type iterative algorithm with mixed errors. Strong convergence theorems of common elements are established in the framework of Hilbert spaces.
Highlights
Variational inclusion has become rich of inspiration in pure and applied mathematics
Classical variational inclusion problems have been extended and generalized to study a large variety of problems arising in image recovery, economics, and signal processing; for more details, see [ – ]
Based on the projection technique, it has been shown that the variational inclusion problems are equivalent to the fixed point problems
Summary
Variational inclusion has become rich of inspiration in pure and applied mathematics. Based on the projection technique, it has been shown that the variational inclusion problems are equivalent to the fixed point problems. This alternative formulation has played a fundamental and significant part in developing several numerical methods for solving variational inclusion problems and related optimization problems. The purposes of this paper is to study the zero point problem of the sum of a maximal monotone mapping and an inverse-strongly monotone mapping, and the fixed point problem of a nonexpansive mapping. In Section , we provide some necessary preliminaries. In Section , a Mann-type iterative algorithm with mixed errors is investigated. Applications of the main results are discussed .
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