A hybrid method for solving variational inequalities over the common fixed point sets of infinite families of nonexpansive mappings in Banach spaces. (English) Zbl 07249890
Summary: In this paper, we introduce a hybrid method, a combination of the steepest-descent method and the Krasnosel’skii-Mann one, for solving a variational inequality over the set of common fixed points of an infinite family of nonexpansive mappings in Banach spaces under two different conditions on the Banach space, either a uniformly smooth Banach space or a reflexive and strictly convex one with a uniformly Gâteaux differentiable norm, without imposing the sequential weak continuity of the normalized duality mapping. The method is an improvement and extension of some other published results. We also give a numerical example to illustrate the convergence analysis of the proposed method.
MSC:
| 47-XX | Operator theory |
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
| 47H17 | Methods for solving equations involving nonlinear operators [See also 58C15] [For numerical analysis, see 65J15] (MSC1991) |
| 47H20 | Semigroups of nonlinear operators |
Keywords:
accretive mappings; fixed points; nonexpansive mappings; hybrid method; variational inequalitiesReferences:
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