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.
De la Sen, M., Ibeas, A., & Herrera, J. (2016). On fixed points and convergence results of sequences generated by uniformly convergent and point-wisely convergent sequences of operators in Menger probabilistic metric spaces. SpringerPlus, 5(1). https://doi.org/10.1186/s40064-016-2057-0