A new iterative method for the split common fixed point problem in Hilbert spaces

Abstract

The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we propose a new algorithm for this problem that is completely different from the existing algorithms. Moreover, our algorithm does not need any prior information of the operator norm. Under standard assumptions, we establish a weak convergence theorem of the proposed algorithm and a strong convergence theorem of its variant.

Keywords:

• Split common fixed point problem
• projection
• variable stepsize
• strong convergence

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11301253] and Program for Science and Technology Innovation Talents in the Universities of the Henan Province [grant number 15HASTIT013].