Abstract
In this work, we establish strong convergence theorems for solving the fixed point problem of nonexpansive semigroups and strict pseudocontractions, and the zero-finding problem of maximal monotone operators in a Hilbert space. We further apply our result to the convex minimization problem and commutative semigroups. MSC: 47H09; 47H10
Highlights
Let H be a real Hilbert space and K a nonempty, closed, and convex subset of H
The fixed points set of T is denoted by F(T)
In this work, motivated by Lau et al [ – ], Marino-Xu [ ], and Saeidi [ ], we introduce a new general iterative scheme for solving the fixed- point problem of a nonexpansive semigroup involving a strict pseudocontraction and the zero-finding problem of a maximal monotone operator in the framework of a Hilbert space
Summary
Let H be a real Hilbert space and K a nonempty, closed, and convex subset of H. In , Mann [ ] introduced the following classical iteration for a nonexpansive mapping T : K → K in a real Hilbert space: x ∈ K and xn+ = αnxn + ( – αn)Txn, n ≥ ,
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