Shrinking projection algorithm for solving a finite family of quasi-variational inclusion problems in Hadamard manifold. (English) Zbl 1476.49013
Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 115, No. 4, Paper No. 166, 11 p. (2021).
Summary: The purpose of this article is to introduce a general shrinking projection algorithm for solving a finite family of quasi-variational inclusion problems in Hadamard manifolds. It is shown that under mild conditions, the sequence generated by the proposed algorithm converges strongly to a common solution to a finite family of quasi-variational inclusion problems. As applications, we apply our results to study a system of variational inequalities in Hadamard manifolds. Our results presented in the paper generalize and improve some recent results.
MSC:
| 49J40 | Variational inequalities |
| 26B25 | Convexity of real functions of several variables, generalizations |
| 47H05 | Monotone operators and generalizations |
| 47J25 | Iterative procedures involving nonlinear operators |
| 58A05 | Differentiable manifolds, foundations |
| 58C30 | Fixed-point theorems on manifolds |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
shrinking projection algorithm; quasi-variational inclusion problem; firmly nonexpansive; maximal monotone vector field; quasi-nonexpansive mappings; Hadamard manifoldReferences:
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