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Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences

  • Chiranjib Choudhury ORCID logo EMAIL logo
Published/Copyright: March 31, 2023

Abstract

Over the last few years, numerous researchers have contributed significantly to summability theory by connecting various notions of convergence concepts of sequences. In this paper, we introduce the concepts of -statistical supremum and -statistical infimum of a real-valued sequence and study some fundamental features of the newly introduced notions. We also introduce the concept of -statistical monotonicity and establish the condition under which an -statistical monotonic sequence is -statistical convergent. We end up giving a necessary and a sufficient condition for the -statistical convergence of a real-valued sequence.

MSC 2020: 40A35; 40A05

Award Identifier / Grant number: 16-6(DEC. 2018)/2019(NET/CSIR)

Funding statement: The author is also grateful to the University Grants Commission, India, for their fellowships funding under the UGC-SRF scheme (No. 16-6(DEC. 2018)/2019(NET/CSIR)) during the preparation of this paper.

Acknowledgements

The author thanks the anonymous referees for their constructive suggestions to improve the quality of the paper.

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Received: 2022-12-09
Revised: 2023-02-22
Accepted: 2023-02-23
Published Online: 2023-03-31
Published in Print: 2023-12-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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