A note on the relationship between the isotone assumption of the AbianBrown fixed point theorem and Abian’s most basic fixed point theoremTools Luckraz, Shravan (2014) A note on the relationship between the isotone assumption of the AbianBrown fixed point theorem and Abian’s most basic fixed point theorem. Fixed Point Theory and Applications, 2014 (1). p. 129. ISSN 16871812
Official URL: https://doi.org/10.1186/168718122014129
AbstractIn a recent paper Xie et al. (Fixed Point Theory Appl. 2013:192, 2013) gave several extensions and some applications of the AbianBrown (AB) fixed point theorem. While the AB fixed point theorem and its extensions (as well as other related fixed point theorems) assume that the mapping is isotone, this note shows that for singlevalued finite maps this condition relates to the acyclicity of the map, which in turn relates to Abian’s (Nieuw Arch. Wiskd. XVI:184185, 1968) most basic fixed point theorem for finite sets.
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