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

Volume 9, Issue 8, pp 5175--5188 Publication Date: August 23, 2016

### Authors

Yang-Qing Qiu - Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China.
Jin-Zuo Chen - Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China.
Lu-Chuan Ceng - Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China.

### Abstract

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.

### Keywords

• Hybrid method
• extragradient method
• proximal method
• zeros
• strong convergence.

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