On quasi 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 by linking different notions of convergence of sequences. In the present paper, we introduce the concept of quasi statistical convergence and strong quasi statistical summability in gradual normed linear spaces. We investigate some of its basic properties and the interrelationship between the newly introduced notions. It has been observed that every gradual quasi statistical convergent sequence is gradual quasi statistical bounded but not necessarily gradual bounded. Finally, we introduce the concept of gradual quasi statistical Cauchy sequences and show that every gradual quasi statistical convergent sequence is a gradual quasi statistical Cauchy sequence.