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We will refer to the paper "Convergence rates for Kaczmarz-type algorithms", published in Numerical Algorithms, 79(1)(2018), 1-17. It was observed by Dr. Mokhtar Abbasi (Department of Mathematics, University of Qom, Iran) that in the proof of Theorem 7, related to the linear convergence rate of the MREK algorithm it exists an inequality which is not always true. [ABSTRACT FROM AUTHOR]