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Revisiting Probabilistic Metric Spaces

International Journal of Topology
The field of probabilistic metric spaces has an intrinsic interest based on a blend of ideas drawn from metric space theory and probability theory. The goal of the present paper is to introduce and study new ideas in this field.
Michael D. Rice
doaj   +3 more sources

Probabilistic modular metric spaces [PDF]

Journal of Hyperstructures, 2020
The purpose of this study is to investigate the connection between probabilistic and modular metric spaces. We discussseveral important properties such as convergence and completeness,etc, and the relationship among the mentioned properties in the ...
Kianoush Fathi Vajargah, Hamid Mottaghi Golshan   +1 more
doaj   +2 more sources

Statistical convergence in probabilistic generalized metric spaces w.r.t. strong topology

Journal of Inequalities and Applications, 2021
In this paper, the concept of probabilistic g-metric space with degree l, which is a generalization of probabilistic G-metric space, is introduced. Then, by endowing strong topology, the definition of l-dimensional asymptotic density of a subset A of N l
Rasoul Abazari
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Fixed point theorem by using ψ–contraction and (ϕ,φ)–contraction in probabilistic 2–metric spaces

Alexandria Engineering Journal, 2020
This research paper investigates and proves some theorems of the fixed point for self–mapping [T:X→X] under (ϕ,ψ)–contractive mappings and (ϕ,φ)–contractive mappings in Menger probabilistic 2–metric space.
H.M. Abu-Donia, H.A. Atia, Omnia M.A. Khater   +2 more
doaj   +2 more sources

Designs in Finite Metric Spaces: A Probabilistic Approach [PDF]

Graphs and Combinatorics, 2021
A finite metric space is called here distance degree regular if its distance degree sequence is the same for every vertex. A notion of designs in such spaces is introduced that generalizes that of designs in Q-polynomial distance-regular graphs.
Minjia Shi, O. Rioul, Patrick Sol'e
semanticscholar   +4 more sources

Probabilistic Generalized Metric Spaces and Nonlinear Contractions

Demonstratio Mathematica, 2016
We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition ...
Mbarki Abderrahim, Naciri Rachid
doaj   +2 more sources

Strong $I^K$-Convergence in Probabilistic Metric Spaces [PDF]

Iranian Journal of Mathematical Sciences and Informatics, 2018
In this paper we study the idea of strong-I^K-convergence of functions which is common generalization of strong-I*-convergence of functions in probabilistic metric spaces. We also study strong-I^K-limit points of functions in the same space.
A. Banerjee, Mahendranath Paul
semanticscholar   +4 more sources

The nonlinear contraction in probabilistic cone b-metric spaces with application to integral equation

Nonlinear Analysis
The probabilistic cone b-metric space is a novel concept that we describe in this study along with some of its fundamental topological properties and instances.
Youssef Achtoun, Stojan Radenović, Ismail Tahiri, Mohammed Lamarti Sefian   +3 more
doaj   +2 more sources

Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces

Journal of Function Spaces, 2015
This paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of ...
Manuel De la Sen, Erdal Karapınar
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Probabilistic convergence spaces and generalized metric spaces [PDF]

International Journal of Mathematics and Mathematical Sciences, 1998
The category PPRS(Δ), whose objects are probabilistic pretopological spaces which satisfy an axiom (Δ) and whose morphisms are continuous mappings, is introduced.
Paul Brock
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