Probabilistic Metric Spaces Research Articles

(1903-5124) Alternative approaches to obtain t-norms and t-conorms on bounded lattices

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defi ned on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods forconstructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for the clarity. Finally, we show that our construction methods can be generalizedby induction to a modi ed ordinal sum for triangular norms and triangular conorms on an arbitrary bounded lattice, respectively.

On ψ-contractions and common fixed point results in probabilistic metric spaces

On ψ-contractions and common fixed point results in probabilistic metric spaces

Common fixed point results for probabilistic φ-contractions in generalized probabilistic metric spaces

Common fixed point results for probabilistic φ-contractions in generalized probabilistic metric spaces

Fixed point results for probabilistic φ -contractions in generalized probabilistic metric spaces

Fixed point results for probabilistic φ -contractions in generalized probabilistic metric spaces

On exhaustive families of random functions and certain types of convergence

A random function of a variable t in T (or, a random function on T) is known as a function f whose values are random variables all defined on a common probability space, where T is an arbitrary set. A random function is also called a stochastic (random) process. In this work, we base ourselves on a random function of E-process type and such a function is also called a random function, briefly. In this approach, the domain of such a random function is or an interval of , and the set of values of this random function is considered as a special probabilistic metric (PM) space (more precisely, an E-space) of metric space-valued random variables, and all our definitions and results are presented using the tools of PM spaces. In this context, we introduce the concept of an exhaustive family of such random functions, which is a natural generalization of equicontinuity, and we investigate its basic properties. We also examine some of the properties related to the continuous convergence in probability for a sequence of such random functions and certain conditions which give rise to the continuity in probability of the limit of a sequence of such random functions.

Statistical Convergence in Probability for a Sequence of Random Functions

In this paper, we introduce a new type of convergence for a sequence of random functions, namely, statistical convergence in probability, which is a natural generalization of convergence in probability. In this approach, we allow such a sequence to go far away from the limit point infinitely many times by presenting random deviations, provided that these deviations are negligible in some sense of measure. In this context, the set of values of a random function is considered as a probabilistic metric (PM) space of random variables, and some basic results are obtained using the tools of PM spaces.

Probabilistic metric spaces determined by measure preserving transformations

Probabilistic metric spaces determined by measure preserving transformations

On E -Spaces and their Relation to Other Classes of Probabilistic Metric Spaces

Journal of the London Mathematical SocietyVolume s1-44, Issue 1 p. 441-448 Notes and papers On E-Spaces and their Relation to Other Classes of Probabilistic Metric Spaces H. Sherwood, H. Sherwood Illinois Institute of Technology, University of Arizona †I want to take this opportunity to thank H. I. Whitlock, A. Sklar and especially B. Schweizer for their invaluable comments and suggestions in the preparation of this manuscript.Search for more papers by this author H. Sherwood, H. Sherwood Illinois Institute of Technology, University of Arizona †I want to take this opportunity to thank H. I. Whitlock, A. Sklar and especially B. Schweizer for their invaluable comments and suggestions in the preparation of this manuscript.Search for more papers by this author First published: 1969 https://doi.org/10.1112/jlms/s1-44.1.441Citations: 36 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volumes1-44, Issue11969Pages 441-448 RelatedInformation

Products and quotients of probabilistic metric spaces

Products and quotients of probabilistic metric spaces