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ANNALES SOCIETATIS MATHEMATICAE POLONAE Series I: COMMENTATIONES MATHEMATICAE X X (1978) ROCZNIKI POLSKIEQO TOWARZYSTWA MATEMATYCZNEGO Séria I: PRACE MATEMATYCZNE X X (1978)

unpublished

A short proof of the Caristi theorem In 1975 Caristi [2] proved a fixed point theorem which was next used in proving some other results [2], [4]. The original proof used the transfinite induction method and was rather complicated. Then several other proofs лГеге found [1], [3], [4], but all of them are more compli cated than the new proof presented below, which uses Zorn's lemma, but in a simple way. T h e o r e m 1 (Wong [4]). Let f be a self map on a non-empty complete metric space (X, d)

fatcat:dn4xqvzqdbdidp2dr73ffg25pe