title: 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 [Formula: see text]-contractions. The definitions of strict (k and [Formula: see text]) 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.
authors.affiliation: Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, PO Box 644, de Bilbao, Barrio Sarriena, 48940 Leioa, Bizkaia Spain.
authors.forename: Manuel
authors.initials: M
authors.lastname: De la Sen
authors.affiliation: Department of Telecommunications and Systems Engineering, Faculty of Engineering, Universitat Autònoma de Barcelona (UAB), 08193 Bellaterra, Cerdanyola del Vallés, Barcelona Spain ; Departamento de Ingeniería, Facultad de Ciencias Naturales e Ingeniería, Universidad de Bogotá Jorge Tadeo Lozano, 22 Street, No. 4-96, Mod. 7A, Bogotá, D.C. 110311 Colombia.
authors.forename: Asier
authors.initials: A
authors.lastname: Ibeas
authors.affiliation: Departamento de Ingeniería, Facultad de Ciencias Naturales e Ingeniería, Universidad de Bogotá Jorge Tadeo Lozano, 22 Street, No. 4-96, Mod. 7A, Bogotá, D.C. 110311 Colombia.
authors.forename: Jorge
authors.initials: J
authors.lastname: Herrera
keywords: Menger spaces; Probabilistic metric spaces; Strict [Formula: see text]-contractions; Strict contractions; Triangular norms