The split common fixed point problem for generalized demimetric mappings in two Banach spaces

ABSTRACT

In this paper, we consider the split common fixed point problem for new demimetric mappings in two Banach spaces. Using the hybrid method, we prove a strong convergence theorem for finding a solution of the split common fixed point problem in two Banach spaces. Furthermore, using the shrinking projection method, we obtain another strong convergence theorem for finding a solution of the problem in two Banach spaces. Using these results, we obtain well-known and new strong convergence theorems in Hilbert spaces and Banach spaces.

KEYWORDS:

• Split common fixed point problem
• fixed point
• metric projection
• metric resolvent
• hybrid method
• shrinking projection method
• duality mapping

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H05
• 47H09

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author was partially supported by Grant-in-Aid for Scientific Research No. 15K04906 from Japan Society for the Promotion of Science.