Some results of variational inclusion problems and fixed point problems with applications

Hao, Yan

doi:10.1007/s10483-009-1210-x

Cited by 9 publications

(2 citation statements)

References 11 publications

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“…Strong convergence theorems of common solutions are established in the framework of Hilbert spaces. The results presented in this paper mainly improve the corresponding results in [13], [15], [16], [30]- [33].…”

Section: Introductionsupporting

confidence: 78%

Iterative common solutions of fixed point and variational inequality problems

Zhang¹,

Yuan²

2016

J. Nonlinear Sci. Appl.

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Section: Introductionsupporting

confidence: 78%

Iterative common solutions of fixed point and variational inequality problems

Zhang¹,

Yuan²

2016

J. Nonlinear Sci. Appl.

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“…For example, the existence and the uniqueness of differential, partial differential, integral, random differential and random integral equations can be obtained using the fixed point method. For detail about fixed point problems and methods (see [7,13,14,23]). Furthermore, a common solution of a VIP (1) and a fixed point problem find applications in real life problems like network resource allocation, image recovery and signal processing (see [2,3,6,26,27,28]).…”

mentioning

confidence: 99%

A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces

Akutsah¹,

Mebawondu²,

Abass³

et al. 2023

NACO

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<p style='text-indent:20px;'>In this work, we propose a new inertial method for solving strongly monotone variational inequality problems over the solution set of a split variational inequality and composed fixed point problem in real Hilbert spaces. Our method uses stepsizes that are generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the operator norm as well as the Lipschitz constant of the operator. In addition, we prove that the proposed method converges strongly to a minimum-norm solution of the problem without using the conventional two cases approach. Furthermore, we present some numerical experiments to show the efficiency and applicability of our method in comparison with other methods in the literature. The results obtained in this paper extend, generalize and improve results in this direction.</p>

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A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities

Jitpeera

2011

International Journal of Mathematics and Mathematical Sciences

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We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu

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Some results of variational inclusion problems and fixed point problems with applications

Cited by 9 publications

References 11 publications

Iterative common solutions of fixed point and variational inequality problems

Iterative common solutions of fixed point and variational inequality problems

A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces

A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities

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