Rough I_((λ,μ) )-Statistical Convergence of Double Sequences in Gradual Normed Linear Spaces

Abstract

The aim of this paper is to we examine the notion of gradually rough I_((λ,μ) )-statistical convergence of double sequences in gradual normed linear spaces (GNLS). In addition, we define the concept of gradually rough I_((λ,μ) )-statistical limit set of double sequences and obtain some algebraic and topological features of this set. Theorems are proved in the light of GNLS theory approach. Results are obtained via different perspective and new examples are established to justify the counterparts and indicate existence of introduced notions. We produce significant results that present several fundamental properties of this notion. The results established in this research work supplies an exhaustive foundation in GNLS and make a significant contribution in the theoretical development of GNLS in literature. The original aspect of this study is the first wholly up-to-date and thorough examination of the features and implementations of new introduced notions in GNLS.