On fixed points and convergence results of sequences generated by uniformly convergent and point‑wisely convergent sequences of operators in Menger probabilistic metric spaces
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Abstract
In the framework of complete probabilistic Menger metric spaces, this paper investigates
some relevant properties of convergence of sequences built through sequences
of operators which are either uniformly convergent to a strict k-contractive operator,
for some real constant k ∈ (0, 1), or which are strictly k-contractive and point-wisely
convergent to a limit operator. Those properties are also reformulated for the case
when either the sequence of operators or its limit are strict -contractions. The definitions
of strict (k and ) contractions are given in the context of probabilistic metric
spaces, namely in particular, for the considered probability density function. A numerical
illustrative example is discussed.
Palabras clave
Strict contractions; Strict ϕ-contractions; Probabilistic metric spaces; Menger spaces; Triangular normsLink to resource
http://doi.org/10.1186/s40064-016-2057-0Collections
- Año 2016 [88]
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