ON QUASI STATISTICAL CONVERGENCE IN GRADUAL NORMED LINEAR SPACES

ON QUASI STATISTICAL CONVERGENCE IN GRADUAL NORMED LINEAR SPACES

C. Choudhury, S. Debnath

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Abstract

During the last few years, enormous works by di erent researchers have been carried out in summability theory by linking di erent notions of convergence of se- quences. In the present paper, we introduce the concept of quasi statistical convergence and strong quasi statistical summability in gradual normed linear spaces. We investi- gate 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 ev- ery gradual quasi statistical convergent sequence is a gradual quasi statistical Cauchy sequence.

Keywords

Gradual number, gradual normed linear space, quasi-density, gradual quasi statistical convergence.