## Tbilisi Mathematical Journal

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

### Double absolute indexed matrix summability with its applications

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

#### 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