Abstract. We generalize various types of F -contractions defined by Wardowski, Vetro and others to b-metric spaces and prove fixed point theorems for them. The examples given show that these generalizations extend the existing results in a significant way.

a b s t r a c tWe prove a Dold-Kan type correspondence between the category of planar dendroidal abelian groups and a suitably constructed category of planar dendroidal chain complexes. Our result naturally extends the classical Dold-Kan correspondence between the category of simplicial abelian groups and the category of non-negatively graded chain complexes.

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In this paper we correct an inaccuracy that appears in the proof of Theorem 1. in Czerwik [1].

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