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

100%

Yao Y., Cho Y., Liou Y.-C.

Open Mathematics

2011

tom 9

nr 3

640-656

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 operator.

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

100%

Petruşel A., Yao J.-C.

Open Mathematics

2009

tom 7

nr 2

335-347

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.

Ograniczanie wyników

2 Open Mathematics

1 Cho Y.

1 Liou Y.-C.

1 Petruşel A.

1 Yao J.-C.

1 Yao Y.

1 2011

1 2009

Wyniki wyszukiwania

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

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