An inertial extragradient algorithm for split problems in Hilbert spaces. (English) Zbl 1522.46049
Summary: In this study, we propose an inertial extragradient algorithm for solving a split generalized equilibrium problem as well as a split feasibility and common fixed point problem. We demonstrate that, under certain reasonable assumptions, the sequences induced by the proposed algorithm converge strongly to a solution of the corresponding problem. In addition, with the help of a numerical example, we demonstrate the efficiency of proposed algorithm. As a result of this paper, some recent well-known results in this area have been improved, generalized, and extended.
MSC:
| 46N10 | Applications of functional analysis in optimization, convex analysis, mathematical programming, economics |
| 47H10 | Fixed-point theorems |
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 65J15 | Numerical solutions to equations with nonlinear operators |
Keywords:
generalized equilibrium problem; nonexpansive mapping; split common fixed point problem; strong convergence; split feasibility problem; extragradient methodReferences:
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