Remarks on a result of L. A. V. Carvalho (Q1895139)

The remarks concern a published result of \textit{L. A. V. Carvalho} [J. Math. Anal. Appl. 138, No. 1, 52-58 (1989; Zbl 0669.26002)]\ on so-called \(n\) step orbits. The authors point out that periodic \(n\)-step orbits were already introduced under the name \(n\)-periodic loops and a stronger result was obtained in \textit{N. P. Bhatia} and \textit{W. O. Egerland} [Proc. Am. Math. Soc. 102, No. 4, 965-972 (1988; Zbl 0651.26004)]. Moreover, the authors give a new simple proof of the result that \((n+1)\)-periodic loop implies the existence of two distinct \(n\)-periodic loops for \(n\geq 3\) and an inequality guaranteeing existence of so-called infinite loop.