Tbilisi Mathematical Journal

Double absolute indexed matrix summability with its applications

B. B. Jena, S. K. Paikray, and U. K. Misra

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Abstract

The well established theory of summability of simple series has been brought to a high degree of development; however the extension of this theory to multiple series is still in its infancy. As regards to the double series, in the proposed paper a result on absolute indexed matrix summability with an additional parameter of doubly infinite lower triangular matrix has been established that generalizes a theorem of E. Savaş and B. E. Rhoades [10] (see E. Savaş and B. E. Rhoades, Double absolute summability factor theorems and applications, Nonlinear Anal. 69 (2008), 189-200). Furthermore, some concluding remarks and applications are presented in support of our result.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 4 (2018), 1-18.

Dates
Received: 4 August 2017
Accepted: 18 June 2018
First available in Project Euclid: 4 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1546570881

Digital Object Identifier
doi:10.32513/tbilisi/1546570881

Mathematical Reviews number (MathSciNet)
MR3954203

Subjects
Primary: 40F05: Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
Secondary: 40D25: Inclusion and equivalence theorems

Keywords
Absolute summability double absolute summability double weighted mean summability factors

Citation

Jena, B. B.; Paikray, S. K.; Misra, U. K. Double absolute indexed matrix summability with its applications. Tbilisi Math. J. 11 (2018), no. 4, 1--18. doi:10.32513/tbilisi/1546570881. https://projecteuclid.org/euclid.tbilisi/1546570881


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References

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