The Strongly Convergent Relaxed Alternating CQ Algorithms for the Split Equality Problem in Hilbert Spaces

Abstract

Recently, Moudafi introduced the split equality problem (SEP): find $x\in C,y\in Q$ such that Ax = By. In this paper, we show that finding a solution of the SEP is equivalent to finding a solution of a coupled fixed-point equation which is an extension of the coupled equation proposed by Yu and Wang. Based on this coupled fixed-point equation, we propose two new relaxed alternating algorithms for the SEP, and we prove that the first relaxed algorithm is weakly convergent and the second is strongly convergent.

Keywords:

• Coupled fixed
• point equation
• relaxed alternating method
• split equality problem

Acknowledgment

The authors would like to express their gratitude to the referee for his or her useful suggestion.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (11601339, 11701154), the Natural Science Foundation of the Department of Education, Henan Province (19A110020, 20A110020), the graduate education reform and quality improvement project of Henan province, higher education teaching reform and practice project (postgraduate education) of Henan Normal University (YJS2019JG01) and Program for Graduate Innovative Research of Henan Normal University (No.YL201919).