zbMATH — the first resource for mathematics

Comments on: Fixed point theorems for \(\varphi\)-contraction in probabilistic metric space. (English) Zbl 1282.54045
Summary: We show that an affirmative answer was already given in [M. El Amrani et al., Panam. Math. J. 11, No. 4, 79–87 (2001; Zbl 1033.54024); A. Mbarki, Quelques aspects de la th\'eorie du point fixe pour les semigroupes. Th\'ese de Doctorat en Sciences, Facult\'e des Sciences, Oujda, Maroc, No. 36/01] to the question raised in [Lj. Ćirić, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No.  3–4, 2009–2018 (2010; Zbl 1194.47093)] and extend a fixed point theorem by Lj. Ćirić [loc. cit.] to a larger class of PM spaces. In the final part of the paper, we show that the result can be yet improved by a common fixed point theorem for semigroups of \(\varphi\)-probabilistic contractions.

54H25 Fixed-point and coincidence theorems (topological aspects)
54E70 Probabilistic metric spaces
Full Text: DOI Link