Weak Almost Iterability

Abstract

We investigate continuous selfmappings of a real compact interval, which are, in a sense, close to iterable ones, that is embeddable into continuous iteration semigroup. This is a continuation of a research initiated by W.~Jarczyk. We present some necessary and sufficient conditions of weak almost iterability and $M-$weak almost iterability. Classes of functions investigated here are generalizations of a class of almost iterable functions introduced by W. Jarczyk. This refers to the problem posed by E.~Jen.