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

Chiranjib Choudhury (1) and Shyamal Debnath (2)

(1,2) Department of Mathematics, Tripura University (A Central University), Suryamaninagar-799022, Agartala, India

Email address: (1) chiranjibchoudhury123@gmail.com

Email address: (2) shyamalnitamath@gmail.com

Doi : https://doi.org/10.47013/15.4.12

Cited by : Jordan J. Math & Stat., 15 (4A) (2022), 967 - 982

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Received on: July 21, 2021;                                              Accepted on: Nov. 4, 2021

 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.

Keywords: Gradual number; gradual normed linear space, I−convergence, I−limit point, I−Cauchy sequence, I−divergence.