Two new self-adaptive algorithms for solving split common fixed point problems with multiple output sets

Abstract

In this paper, we study split common fixed point problems with multiple output sets in Hilbert spaces. For solving this problem, we improve Reich and Tuyen's algorithms [10] and propose two new self-adaptive algorithms which do not need any priori information on the norms of the transfer operators. Then, we establish weak convergence theorems for them. It can be seen from our numerical experiments that the proposed methods depict a very significant improvement in terms of the number of iterations and execution time.

Keywords:

• Split common fixed point
• multiple output sets
• self-adaptive algorithm
• quasinonexpansive mapping

Mathematics Subject Classification 2010:

• Primary 47H09
• 47H10
• 49J53
• 90C25

Acknowledgments

The authors equally conceived of the study, participated in its design and coordination, drafted the manuscript, participated in the sequence alignment, and read and approved the final manuscript.

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 62103289], National Natural Science Foundation of China [grant number 11761074] and Natural Science Foundation of Jilin Province [grant number 2020122336JC].