Mixed iterative algorithms for the multiple-set split equality common fixed-point problems without prior knowledge of operator norms

Abstract

Let , , be real Hilbert spaces, let , be two bounded linear operators. The multiple-set split equality common fixed-point problem (MSECFP) under consideration in this paper is to(Section.Display)

where are integers, and are quasi-nonexpansive mappings with nonempty fixed-point sets. Note that, the above problem (1) allows asymmetric and partial relations between the variables and . If and , then the MSECFP (1) reduces to the multiple-set split common fixed-point problem proposed by Censor et al. In this paper, we introduce mixed cyclic and simultaneous iterative algorithms for the MSECFP (1). We introduce a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. Weak convergence results are given.

Keywords:

• the multiple-set split equality common fixed-point problem
• quasi-nonexpansive mapping
• weak convergence
• iterative algorithms
• Hilbert space

AMS Subject Classifications:

• 47H09
• 47H10
• 47J05
• 54H25

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported by Fundamental Research Funds for the Central Universities [Program No. 3122015L013].