A new self-adaptive method for the split equality common fixed-point problem of quasi-nonexpansive mappings

ABSTRACT

In this paper, we introduce a new iterative algorithm from primal-dual methods for solving the split equality common fixed-point problem of quasi-nonexpansive mappings in real Hilbert space. Our algorithm includes the simultaneous iterative algorithm as special case which has been proposed by Moudafi and Al-Shemas for solving the split equality common fixed-point problem. We use a way of selecting the stepsizes such that the implementation of our algorithm does not need any prior information about bounded linear operator norms. It avoids the difficult task of estimating the operator norms. Under suitable conditions, we get the weak convergence of the proposed algorithm. The performance of the proposed algorithm is also illustrated by preliminary numerical experiments. The results presented in the paper improve and extend some corresponding results.

Keywords:

• Split equality common fixed-point problem
• split feasibility problem
• quasi-nonexpansive mapping
• primal-dual algorithm
• weak convergence

AMS Mathematics Subject Classifications:

• 47H09
• 47H10
• 47J05
• 54H25

Acknowledgments

The authors thank the editors and reviewers for their helpful comments.

Disclosure statement

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

Additional information

Funding

Supported by the Fundamental Research Funds for the Central Universities (No. 3122019191).