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The inequalities (2.17), (2.23), (2.25) and (2.27) in [1] are not valid. Figure 1 in [1] remains correct. Recently, I found out, that the article [1] contains errors. To be precise, the inequalities (2.17), (2.23), (2.25) and (2.27) in [1] are incorrect. Their proofs contain errors. It is clear from [2, p. 324] that these problems were known to the first author of [1] as early as March 2009. Instead of publishing an erratum the first author of [1] discussed the problems with a third person, and published the article [2] in this journal, without informing his coauthor about it until August 20th, 2010. The first author of [1] states in the title and abstract of [2], that in [2] “the obtained inequalities improve certain bounds derived recently in” [1] (see [2, p. 315]). This is misleading, because those bounds in [1] were never valid. In [2] the first author of [1] states also, that his second article [2] “is essentially not a corrigendum to [1]” (see [2, p. 315]). Again, this statement is not true. It contradicts the remarks on pages 320, 321, 322 and 323 in [2]. With this erratum I disagree with these statements of my coauthor. I herewith distance myself from the entire article [1] except for those results, that I contributed personally to [1], and maintain that the inequalities S 2 (r;{n}n=1) M(r,2) S 2 (r;{n}n=1) M(r,2) S 2 ( r; { n }∞ n=1 ) M(r,2) for 0 < r < 3, illustrated in Figure 1 [1, p.25], remain correct. Mathematics subject classification (2010): 26D15, 33C60, 33E20, 44A20.

Erratum on "Some bounds for alternating Mathieu type series"