TY - JOUR
T1 - On fixed points and convergence results of sequences generated by uniformly convergent and point-wisely convergent sequences of operators in Menger probabilistic metric spaces
AU - De la Sen, Manuel
AU - Ibeas, Asier
AU - Herrera, Jorge
PY - 2016/12/1
Y1 - 2016/12/1
N2 - © 2016, De la Sen et al. 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 φ-contractions. The definitions of strict (k and φ) 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.
AB - © 2016, De la Sen et al. 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 φ-contractions. The definitions of strict (k and φ) 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.
KW - Menger spaces
KW - Probabilistic metric spaces
KW - Strict contractions
KW - Strict φ-contractions
KW - Triangular norms
UR - https://ddd.uab.cat/record/185885
U2 - https://doi.org/10.1186/s40064-016-2057-0
DO - https://doi.org/10.1186/s40064-016-2057-0
M3 - Article
VL - 5
IS - 1
M1 - 557
ER -