Further Results on I and I*−Convergence of Sequences in Gradual Normed Linear Spaces

Abstract

In this paper, following a very recent and new approach, we introduce the notion of gradual I−limit point, gradual I−cluster point, and prove certain properties of both the notions. We also investigate some new properties of gradual I−Cauchy and gradual I*−Cauchy sequences and show that the condition (AP) plays a crucial role to relate both the notions. Finally, we investigate the notion of I and I*−divergence of sequences in gradual normed linear spaces and prove the essence of the condition (AP) again to establish the relationship between the notions.

Key words and phrases. Gradual number; gradual normed linear space, I−convergence, I−limit point, I−Cauchy sequence, I−divergence.

2020 Mathematics Subject Classification. 40A35, 03E72, 40A05