Split common fixed point and null point problems for demicontractive operators in Hilbert spaces

Abstract

In this article, we consider a split common fixed point and null point problem which includes the split common fixed point problem, the split common null problem and other problems related to the fixed point problem and the null point problem. We introduce an algorithm for studying the split common fixed point and null problem for demicontractive operators and maximal monotone operators in real Hilbert spaces. We establish a strong convergence result under some suitable conditions and reduce our main result to above-mentioned problems. Moreover, we also apply our main results to the split equilibrium problem. Finally, we give numerical results to demonstrate the convergence of our algorithms.

Keywords:

• split common fixed point problems
• split null point problems
• demicontractive operators
• maximal monotone operators
• resolvent operators
• strong convergence

Mathematics Subject Classification:

• 47H05
• 47H09
• 47J25

Acknowledgments

The authors would like to thank the referees for valuable comments and suggestions for improving this work. We also would like to thank the Thailand Research Fund and Chiang Mai University for the financial support. The first author was supported by the Royal Golden Jubilee (RGJ) PhD Programme.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The Thailand Research Fund under the project RTA 5780007, Chiang Mai University and the Royal Golden Jubilee (RGJ) PhD Programme.