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Some aspects of 𝜆-weak convergence using difference operator

  • Archana Sharma , Reena Kumari EMAIL logo and Vijay Kumar
Published/Copyright: August 8, 2024

Abstract

In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator Δ ı ȷ and the de la Vallée–Poussin mean, denoted as [ ( V , λ ) w , Δ ı ȷ ] m for m = 0 , 1, and ∞. Further, we explore some algebraic and topological properties of these spaces, including their nature as linear, normed, Banach, and BK spaces. Additionally, we examine properties such as solidity, symmetry, and monotonicity. Finally, we define and establish some inclusion relations among generalized difference weak statistical convergence, generalized difference weak 𝜆-statistical convergence, and generalized difference weak [ V , λ ] -convergence.

MSC 2020: 40G15; 46B45; 39A70

Acknowledgements

We would like to thank the reviewers for their careful reading, which improved the presentation of paper.

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Received: 2024-06-11
Revised: 2024-07-19
Accepted: 2024-07-23
Published Online: 2024-08-08

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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