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Qing Yuan, Strong convergence of a viscosity method for relaxed cocoercive variational inequalities and a finite family of nonexpansive mappings, Eur. J. Math. Appl. 6 (2026), Article ID 11.

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Volume 6 (2026), Article ID 11

https://doi.org/10.28919/ejma.2026.6.11

Published: 02/10/2026

Abstract:

In this paper, we introduce a viscosity-type iterative algorithm with two projection steps for finding a common element of the solution set of a variational inequality involving a relaxed $(u,v)$-cocoercive and $\mu$-Lipschitz continuous mapping and the common fixed point set of a finite family of nonexpansive mappings in a real Hilbert space. The finite family of nonexpansive mappings is treated by means of the $W$-mapping. Under suitable conditions on the control sequences, we prove that the sequence generated by the algorithm converges strongly to a common element $q$, which is the unique solution of the variational inequality $\langle (I-f)q,p-q\rangle\geq 0$ for all $p$ in the common solution set, where $f$ is a contraction.

How to Cite:

Qing Yuan, Strong convergence of a viscosity method for relaxed cocoercive variational inequalities and a finite family of nonexpansive mappings, Eur. J. Math. Appl. 6 (2026), Article ID 11. https://doi.org/10.28919/ejma.2026.6.11