FURTHER RESULTS ON I AND I* -CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

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.