A modified viscosity iterative method for implicit midpoint rule for optimization and fixed point problems in CAT(0) spaces. (English) Zbl 1518.47098
Summary: In this paper, we introduce a proximal point-type of viscosity iterative method with double implicit midpoint rule comprising of a nonexpansive mapping and the resolvents of a monotone operator and a bifunction. Furthermore, we establish that the sequence generated by our proposed algorithm converges strongly to an element in the intersection of the solution sets of monotone inclusion problem, equilibrium problem and fixed point problem for a nonexpansive mapping in complete \(\mathrm{CAT}(0)\) spaces. In addition, we give a numerical example of our method each in a finite dimensional Euclidean space and a non-Hilbert space setting to show the applicability of our method. Our results complement many recent results in the literature.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H06 | Nonlinear accretive operators, dissipative operators, etc. |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E50 | Complete metric spaces |
Keywords:
viscosity iterative method; strong convergence; implicit midpoint rule; monotone inclusion problem; equilibrium problem; fixed point problem; Hadamard spaceReferences:
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