Abstract
Srivastava and Singh [9] generalized the idea of \(\Lambda\)-strong convergence given by Móricz [6] to T-strong convergence of numerical sequences and Fourier series. In this present work, we introduce the idea of Tr-strong convergence \(r\in\mathbb{N}\), by generalizing the idea of T-strong convergence. This paper also generalizes some results of Kórus [5], as shown in conclusion. Additionally, we provide a relationship between T-strong convergence, T2-strong convergence, \(\dots\), Tr-strong convergence, and ordinary convergence. We also demonstrate that this idea can be used to explain the Tr-convergence of Fourier series in the C-metric and the Lp-metric.
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This work was supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India [Award No. 09/1007(0008)/2020-EMR-I], and Sardar Vallabhbhai National Institute of Technology, Surat-395007, Gujarat [Grant No. 2020-21/Seed Money/26].
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Devaiya, S., Srivastava, S.K. ON Tr-strong convergence of numerical sequences and Fourier series. Acta Math. Hungar. 169, 277–288 (2023). https://doi.org/10.1007/s10474-023-01302-0
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DOI: https://doi.org/10.1007/s10474-023-01302-0