The split common null point problem and the shrinking projection method in Banach spaces

Abstract

In this paper, we consider the split common null point problem with resolvents of maximal monotone operators in Banach spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a solution of the split common null point problem in Banach spaces.

Keywords:

• split common null point problem
• maximal monotone operator
• fixed point
• metric resolvent
• shrinking projection method
• duality mapping

AMS Subject Classifications:

• 47H05
• 47H09

Disclosure Statement

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

Additional information

Funding

The second author was partially supported by Grant-in-Aid for Scientific Research No. 23540188 from Japan Society for the Promotion of Science.