Strong convergence algorithm for the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem. (English) Zbl 1540.47094
Summary: The purpose of this paper is to recommend an iterative scheme to approximate a common element of the solution sets of the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem for non-expansive mappings. We prove that the sequences generated by the recommended iterative scheme strongly converge to a common element of solution sets of stated split problems. In the end, we provide a numerical example to support and justify our main result. The result studied in this paper generalizes and extends some widely recognized results in this direction.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47J22 | Variational and other types of inclusions |
| 47H05 | Monotone operators and generalizations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
nonexpansive mapping; split feasibility problem; averaged mapping; split variational inclusion problem; split generalised equilibrium problem; fixed point problem; iterative scheme; strong convergenceReferences:
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