Strong convergence for a common solution of variational inequalities, fixed point problems and zeros of finite maximal monotone mappings
Authors
YangQing Qiu
 Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China.
JinZuo Chen
 Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China.
LuChuan 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 Manntype
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.
MSC
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