New Observations on Lacunary I-Invariant Convergence for Sequences in Fuzzy Cone Normed Spaces

Abstract

The intention of this chapter is to examine some recent development in fuzzy cone normed linear spaces (FCNS in short) and its applications. More recently, features of FCNS and some convergence types for ordinary (single) sequences in FCNS have been worked. First, we introduce the concepts of lacunary I-invariant convergence, I-invariant statistical convergence, lacunary I-invariant statistical convergence for sequences in FCNS. Then, I???-limit points and I??-cluster points of sequences in FCNS are examined. In addition, I??-Cauchy and I??*-Cauchy sequences in FCNS are presented. In FCNS, we establish several properties of new types of convergences and prove various correlation theorems. © 2023 Elsevier B.V., All rights reserved.