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


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.


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ISRP Style

Yang-Qing Qiu, Jin-Zuo Chen, Lu-Chuan Ceng, Strong convergence for a common solution of variational inequalities, fixed point problems and zeros of finite maximal monotone mappings, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 8, 5175--5188

AMA Style

Qiu Yang-Qing, Chen Jin-Zuo, Ceng Lu-Chuan, Strong convergence for a common solution of variational inequalities, fixed point problems and zeros of finite maximal monotone mappings. J. Nonlinear Sci. Appl. (2016); 9(8):5175--5188

Chicago/Turabian Style

Qiu, Yang-Qing, Chen, Jin-Zuo, Ceng, Lu-Chuan. "Strong convergence for a common solution of variational inequalities, fixed point problems and zeros of finite maximal monotone mappings." Journal of Nonlinear Sciences and Applications, 9, no. 8 (2016): 5175--5188


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