Block‐iterative schemes for the split common fixed point problem and applications

Abstract

In this paper, based on the extrapolated Landweber‐type operators, we present new strongly convergent block‐iterative schemes for solving the split common fixed point problem (SCFPP) with demiclosed strongly quasi‐nonexpansive operators on Hilbert spaces. The strong convergence is proved without the additional assumptions such as the boundedly regular condition and the closedness property of the range of the transformation operator, assumed recently in the literature for the problem. A necessary and sufficient condition that ensures that a th iterate is a solution is given. An application of our results to solve the multiple‐sets split convex feasibility problem (MSSCFP) is showed with computational experiments for illustration.