The aim of this work is to introduce new classes of functions called Stepanov-Orlicz ergodic functions, which generalize in a natural way the classical Stepanov ergodicity introduced by Diagana. Comparative study of these new functions is investigated. Examples and counterexamples are presented.

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Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz

In the present paper, we give criteria for the existence of extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm. Some properties of the set of attainable points of the Amemiya norm in this space are also discussed.