On fixed points and convergence results of sequences generated by uniformly convergent and point-wisely convergent sequences of operators in Menger probabilistic metric spaces

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.

Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

“…We can see this result in the proof of Theorems 1 and 2 in [16] and [34], respectively. [15].) The following properties hold:…”

“…In this way, the existence of a fixed point for infinite families of self-mappings of a complete metric space satisfying some new conditions of common contractivity was studied by Allahyari et al in [3]. Also, the study on fixed point and convergence of sequences generated by a family of k-contractions and ϕ-contractions in Menger spaces was worked by De la Sen et al in [15].…”