A note on φ-contractions in probabilistic and fuzzy metric spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 2017 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 313, pages 119-121 (issn: 0165-0114,

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Authors: Carmen Alegre; Salvador Romaguera;

doi: 10.1016/j.fss.2016.06.014

A note on φ-contractions in probabilistic and fuzzy metric spaces

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Abstract

[EN] In a recent paper Fang (2015) [1], J.X. Fang generalized a crucial fixed point theorem for probabilistic phi-contractions on complete Menger spaces due to Jachymski (2010) [3]. In this note we show that actually Fang s theorem is an easy consequence of Jachymski s theorem. We also observe that the proof of a fixed point theorem for complete metric spaces deduced by Fang from his main result is not correct and present a new proof of it.

Related Organizations

Universitat Politècnica de València
Spain

Keywords

Fixed point, Probabilistic phi-contraction, MATEMATICA APLICADA, Complete Menger space

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