Mixed iterative algorithms for the multiple-set split equality common fixed-point problems without prior knowledge of operator norms. (3rd May 2016) - Zhao, Jing; Wang, Shengnan
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.