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On double absolute factorable matrix summability. (English) Zbl 1383.40011
Summary: In this article a new result \(|A, p_m, q_n;\delta|_k\) on summability of doubly infinite lower triangular matrix has been established which generalizes a theorem of E. Savaş and B. E. Rhoades [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 1, 189–200 (2008; Zbl 1167.40302)] and subsequently a theorem of S. K. Paikray, P. K. Das, P. N. Samanta, M. Misra and U. K. Misra [“Double absolute matrix summability methods”, in: 5th Int. Conf. Latest Innov. Sci. Eng. Manag. (ICLISEM 2017), 153–164 (2017), http://data.conferenceworld.in/ICLISEM5/P153-164.pdf] on summability factor of double infinite weighted mean matrix.

MSC:
40F05 Absolute and strong summability
40D15 Convergence factors and summability factors
40G99 Special methods of summability
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References:
[1] 1. B.E. Rhoades, On absolute normal double matrix summability methods, Glasnik mathematicki, Vol. 38(58)(2003), 57-73. · Zbl 1040.40002
[2] 2. B. B. Jena, S. K. Paikray, U. K. Misra, Double Absolute Indexed Matrix Summability and Applications, International Journal of Pure and Applied Mathematics, (Accepeted) · Zbl 1413.42008
[3] 3. E. Savaş, B.E. Rhoades, Double absolute summability factor theorems and applications, Nonlinear Analysis, Vol. 69, pp. 189-200, (2008). · Zbl 1167.40302
[4] 4. S.K. Paikray, P.K. Das, P.N. Samanta, M. Misra and U.K. Misra, Double Absolute Matrix Summability Methods, under communication.
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