Displaying similar documents to “Algorithm for solving a generalized mixed equilibrium problem with perturbation in a Banach space.”

Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems

Yonghong Yao, Yeol Cho, Yeong-Cheng Liou (2011)

Open Mathematics

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In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear...

An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

Adrian Petruşel, Jen-Chih Yao (2009)

Open Mathematics

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In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.