On weighted statistical convergence in gradual normed linear spaces

Abstract

During the last few years, enormous works by different researchers have been carried out in summability theory through investigating various notions of convergence of sequences. In the present paper, we introduce the concept of weighted $g$-statistical convergence in the gradual normed linear spaces. We investigate a few fundamental properties and establish some implication relations. Finally, we introduce the concept of gradual weighted $g$-statistical Cauchy sequences and show that every gradual weighted $g$-statistically convergent sequence is a gradual weighted $g$-statistical Cauchy sequence and vice versa.