ISSN 1686-0209 Thai Journal of Mathematics Volume 20 Number 4 (2022) Pages 1707–1719 http://thaijmath.in.cmu.ac.th Rough Statistical Convergence in Probabilistic Normed Spaces Reena Antal 1,* , Meenakshi Chawla 1 and Vijay Kumar 2,3 1 Department of Mathematics, Chandigarh University, Mohali, Punjab, India e-mail : reena.antal@gmail.com (R. Antal); chawlameenakshi7@gmail.com (M. Chawla) 2 Department of Mathematics, Panipat Institute of Engineering and Technology, Panipat, Haryana, India 3 Department of Mathematics, Chandigarh University, Mohali, Punjab, India e-mail : vjy kaushik@yahoo.com (V. Kumar) Abstract The main purpose of this work is to define rough statistical convergence in probabilistic normed spaces. We have proved some basic properties as well as some examples which shows this idea of convergence in probabilistic normed spaces is more generalized as compared to the rough statistical convergence in normed linear spaces. Further, we have shown the results on sets of statistical limit points and sets of cluster points of rough statistically convergent sequences in these spaces. MSC: 40A05; 26E50; 40G99 Keywords: statistical convergence; rough statistical convergence; probablistic normed space Submission date: 17.03.2020 / Acceptance date: 25.08.2020 1. Introduction In 1951, Fast[1] presented a new idea of convergence named as statistical convergence that is more generalized than the usual convergence for the sequences. Definition 1.1. [1] A sequence x = {x k } of numbers is said to be statistically convergent to ξ if for every ǫ> 0 we have lim n→∞ 1 n |M (x, ǫ)| = δ(M (x, ǫ)) = 0, where |M (x, ǫ)| represents the order of the enclosed set M (x, ǫ)= {k ≤ n : |x k − ξ |≥ ǫ}. An interesting generalization of usual convergence named as rough convergence was initially introduced by Phu[2] for the sequences on finite dimensional normed linear spaces and later on introduced on infinite dimensional normed linear spaces[3]. He mainly worked on rough limits, roughness degree, rough continuity of linear operators and also introduced rough Cauchy sequences. Definition 1.2. [2] A sequence x = {x k } in a normed linear space (X, ‖.‖) is said to be rough convergent to ξ ∈ X for some non-negative number r if for every ǫ> 0 there exists k 0 ∈ N such that ‖x k − ξ ‖ <r + ǫ for all k ≥ k 0 . *Corresponding author. Published by The Mathematical Association of Thailand. Copyright c  2022 by TJM. All rights reserved.