I-limit points and I-cluster points of multiset sequences

Abstract

I-convergence is a type of convergence that generalizes many known types of convergences. In this study, I-convergence and I-boundedness of multiset sequences are defined and some examples are given. I-limit points, I-cluster points, B_mx and A_mx sets and the concepts of I-limit infimum and I-limit supremum are defined for a multiset sequence. These definitions are supported by examples. It is shown that the set of I-cluster points of a multiset sequence covers the set of I-limit points and I-lim inf mx ≤ I-lim sup mx. Additionally, necessary and sufficient conditions for I-lim inf mx = I-lim sup mx are proved.