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# On Arithmetic Means of Sequences Generated by a Periodic Function

In this paper we prove the convergence of arithmetic means of sequences generated by a periodic function $\varphi (x)$, moreover if $\varphi (x)$ satisfies a suitable symmetry condition, we prove that their limit is $\varphi (0)$. Applications of previous results are given to study other means of sequences and the behaviour of a class of recursive series.