On fixed point theorems involving altering distances in Menger probabilistic metric spaces (original) (raw)
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Comments on ’Fixed Point Theorems for ϕ-Contraction in Probabilistic Metric Space’
In this work we have shown that an affirmative answer was already given in [1, 5] to the question raised in [4] and have extended a fixed point theorem by L.Ćirić [4] to a larger class of PM spaces. In the final part of the paper we have shown that the result can be yet improved by a common fixed point theorem for a semigroups of ϕ-probabilistic contractions.
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The notion of a ⌿, C-contraction type multivalued mapping is introduced. This notion is a generalization of the notion of C-contraction introduced by T. L. Hicks Ž. Uni¨. u No¨om Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 13, 1983, 63᎐72. A Ž. fixed point theorem for ⌿, C-contraction is proved. An application on the existence of a random fixed point for random operator f : M = ⍀ ª M, where Ž. Ž. M,d is a separable metric space and ⍀, A A, m a measure space with a decom-Ž. posable measure of NSA-type, is given.