Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Remarks on microperiodic multifunctions447459771ENJ.OlkoAGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland.Journal Article20140220It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.<br /><br />Stability of microperiodic multifunctions is considered, namely we show that an approximately microperiodic multifunction is close to a constant one, provided it is continuous at some point. As a consequence we obtain stability result for an approximately microperiodic single-valued function.http://bims.iranjournals.ir/article_771_daeaa7f55c0826ade1687602332086b4.pdf