# Iterative algorithms for the split variational inequality and fixed point problems under nonlinear transformations

Volume 10, Issue 2, pp 843--854
Publication Date: February 20, 2017 Submission Date: October 11, 2016
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### Authors

Yonghong Yao - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China. Yeong-Cheng Liou - Department of Healthcare Administration and Medical Informatics; and Research Center of Nonlinear Analysis and Optimization and Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan. Jen-Chih Yao - Center for General Education, China Medical University, Taichung, 40402, Taiwan.

### Abstract

In the present paper, we consider the split variational inequality and fixed point problem that requires to find a solution of a generalized variational inequality in a nonempty closed convex subset $\mathcal{C}$ of a real Hilbert space $\mathcal{H}$ whose image under a nonlinear transformation is a fixed point of a pseudocontractive operator. An iterative algorithm is introduced to solve this split problem and the strong convergence analysis is given.

### Share and Cite

##### ISRP Style

Yonghong Yao, Yeong-Cheng Liou, Jen-Chih Yao, Iterative algorithms for the split variational inequality and fixed point problems under nonlinear transformations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 843--854

##### AMA Style

Yao Yonghong, Liou Yeong-Cheng, Yao Jen-Chih, Iterative algorithms for the split variational inequality and fixed point problems under nonlinear transformations. J. Nonlinear Sci. Appl. (2017); 10(2):843--854

##### Chicago/Turabian Style

Yao, Yonghong, Liou, Yeong-Cheng, Yao, Jen-Chih. "Iterative algorithms for the split variational inequality and fixed point problems under nonlinear transformations." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 843--854

### Keywords

• Split problem
• variational inequality
• fixed point
• iterative algorithm
• pseudocontractive mappings.

•  49J53
•  49M37
•  65K10
•  90C25

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