Splitting methods for monotone operators and bifunctions

Volume 9, Issue 6, pp 3939--3947 http://dx.doi.org/10.22436/jnsa.009.06.41

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Authors

Yan Hao - School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China. - Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, Zhejiang 316022, China. Zhisong Liu - School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, China. - Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, Zhejiang 316022, China. Sun Young Cho - School of Mathematics, Gyeongsang National University, Jinju 660-701, Korea.

Abstract

The purpose of this article is to investigate fixed point problems of a nonexpansive mapping, solutions of quasi variational inclusion problem, and solutions of a generalized equilibrium problem based on a splitting method. Our convergence theorems are established under mild restrictions imposed on the control sequences. The main results improve and extend the recent corresponding results.

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Keywords

• Variational inclusion
• monotone operator
• operator equation
• bifunction
• convergence.

MSC

•  65J15
•  90C33

References

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