Tbilisi Mathematical Journal

Sufficient conditions for infinite series by absolute $\varphi$-product summable factor

Smita Sonker and Alka Munjal

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Absolute Cesàro-Riesz summability method has been introduced and later on used to established a theorem containing least set of sufficient conditions for absolute $\varphi$-Cesàro-Riesz summable factor of an infinite series. The result has also been validated with the published literature on $ \varphi-|\bar{N}, p_n|_k$ summable factor by reducing certain conditions in the presented result.


The authors express their sincere gratitude to the Department of Science and Technology (India) for providing financial support to the second author under INSPIRE Scheme (Innovation in Science Pursuit for Inspired Research Scheme).

Article information

Tbilisi Math. J., Volume 12, Issue 4 (2019), 29-41.

Received: 15 April 2019
Accepted: 23 September 2019
First available in Project Euclid: 3 January 2020

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 40F05: Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
Secondary: 40D15: Convergence factors and summability factors 40G05: Cesàro, Euler, Nörlund and Hausdorff methods

absolute summability Cesàro-Riesz mean infinite series positive non-decreasing sequence


Sonker, Smita; Munjal, Alka. Sufficient conditions for infinite series by absolute $\varphi$-product summable factor. Tbilisi Math. J. 12 (2019), no. 4, 29--41. doi:10.32513/tbilisi/1578020565. https://projecteuclid.org/euclid.tbilisi/1578020565

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