# A generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces

Volume 10, Issue 9, pp 4890--4900
Publication Date: September 22, 2017 Submission Date: May 25, 2017
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### Authors

Shih-Sen Chang - Center for General Education, China Medical University, Taichung, 40402, Taiwan. - College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China. Ching-Feng Wen - Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University , Kaohsiung 80702, Taiwan. - Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80702, Taiwan. Jen-Chih Yao - Center for General Education, China Medical University, Taichung, 40402, Taiwan. Jing-Qiang Zhang - College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China.

### Abstract

A generalized forward-backward method for solving split equality quasi inclusion problems of accretive operators in Banach spaces is studied. Some strong convergence theorems for the sequences generalized by the algorithm to a solution of quasi inclusion problems of accretive operators are proved under certain assumptions. The results presented in this paper are new which extend and improve the corresponding results announced in the recent literatures. At the end of the paper some applications to monotone variational inequalities, convex minimization problem, and convexly constrained linear inverse problem are presented.

### Share and Cite

##### ISRP Style

Shih-Sen Chang, Ching-Feng Wen, Jen-Chih Yao, Jing-Qiang Zhang, A generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4890--4900

##### AMA Style

Chang Shih-Sen, Wen Ching-Feng, Yao Jen-Chih, Zhang Jing-Qiang, A generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces. J. Nonlinear Sci. Appl. (2017); 10(9):4890--4900

##### Chicago/Turabian Style

Chang, Shih-Sen, Wen, Ching-Feng, Yao, Jen-Chih, Zhang, Jing-Qiang. "A generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4890--4900

### Keywords

• Generalized forward-backward method
• accretive operator
• $m$-accretive operator
• maximal monotone operator
• split equality quasi inclusion problem

•  47H09
•  47H10
•  47N10

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