Strong convergence for a common solution of variational inequalities, fixed point problems and zeros of finite maximal monotone mappings

Qiu, Yang-Qing¹ ; Chen, Jin-Zuo¹ ; Ceng, Lu-Chuan¹

¹ Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 8, p. 5175-5188.

Résumé

In this paper, by the strongly positive linear bounded operator technique, a new generalized Mann-type hybrid composite extragradient CQ iterative algorithm is first constructed. Then by using the algorithm, we find a common element of the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping, the set of zeros of two families of finite maximal monotone mappings and the set of fixed points of an asymptotically $\kappa$-strict pseudocontractive mappings in the intermediate sense in a real Hilbert space. Finally, we prove the strong convergence of the iterative sequences, which extends and improves the corresponding previous works.

Détail

DOI : 10.22436/jnsa.009.08.03

Classification : 47J25, 47H05, 49J40, 49J53
Keywords: Hybrid method, extragradient method, proximal method, zeros, strong convergence.

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