New algorithms for the split common null point problem

ABSTRACT

Two new iterative algorithms are introduced for solving the split common null point problem (SCNPP). The first algorithm is shown to converge weakly and the second is shown to converge strongly to a solution of SCNPP in a Hilbert space. The algorithms are forward methods (i.e, involving no computation of the resolvent of a monotone operator). Another feature of the algorithms is that the selection of the step-sizes does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms.

Keywords:

• Split common null point problem
• monotone mapping
• weak convergence
• strong convergence

2000 Mathematics Subject Classifications:

• 65K10
• 65K05
• 47H10
• 47L25

Acknowledgments

The authors express their deep gratitude to the referee and the editor for his/her valuable comments and suggestions. We would also like to thank Professor HongKun Xu in particular for his help in writing and many useful discussions, which have greatly improved our manuscript. This article was funded by the Natural Science Foundation of Chongqing (CSTC2019JCYJ-msxmX0661), Science and Technology Research Project of Chongqing Municipal Education Commission (KJQN 201900804) and the Research Project of Chongqing Technology and Business University (KFJJ1952007).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This article was funded by the Natural Science Foundation of Chongqing [CSTC2019JCYJ-msxmX0661], Scientific and Technological Research Program of Chongqing Municipal Education Commission [KJQN 201900804] and the Research Project of Chongqing Technology and Business University [KFJJ1952007].