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In this article the notion of acceleration convergence of double sequences in Pringsheim’s sense has been introduced and some theorems related to that concept have been established using the four dimensional matrix transformations.
Czasopismo
Rocznik
Tom
Strony
85--92
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Department of Mathematics Rajiv Gandhi University Rono Hills, Doimukh-791 112 Arunachal Pradesh, India
Bibliografia
- [1] BREZINSKI C., Convergence acceleration during the 20th century, Your. Comput. Appl. Math., 122(1999), 1-21.
- [2] Brezinski C., Delahaye J.P., Ggermain-Bonne B., Convergence acceleration by extraction of linear subsequences, SIAM Jour. Numer. Anal., 20(1983), 1099-1105.
- [3] Dawson D.F., Matrix summability over certain classes of sequences ordered with respect to rate of convergence, Pacific Jour. Math., 24(1),(1968), 51-56.
- [4] Hamilton H.J., Transformation of multiple sequences, Duke Math. Jour., 2(1936), 29-60.
- [5] Hamilton H.J., A generalization of multiple sequence transformation, Duke Math. Jour., 4(1938), 343-358.
- [6] Keagy T.A., Ford W.F., Acceleration by subsequence transformation, Pacific Jour. Math., 132(1)(1988), 357-362.
- [7] Patterson R.F., Analogues of some fundamental theorems of summability theory, International Jour.Math. and Math. Sci., 23(1)(2000), 1-9.
- [8] Patterson R.F., Rate of convergence of double sequences, Southeast Asian Buli. Math., 26(2002), 469-478.
- [9] Pringsheim A., Zur theorie der zweifach unendlichen zahlenfolgen, Mathematische Annalen, 53(1900), 289-321.
- [10] Robinson G.M., Divergent double sequences and series, Trans. Amer. Math. Soc., 28(1926), 50-73.
- [11] Rooser J.B., Transformation to speed the convergence of series, Jour. Res. Nat. Bur. Stands, 46(1)(1951), 56-64.
- [12] Salzer H.E., A simple method for summing certain slowly convergent series, Jour. Math. Phys., 33(1955), 356-369.
- [13] Smith D.A., Ford W.F., Acceleration of linear and logarithmic convergence, SIAM Jour. Numer. Anal., 16(2)(1979), 223-240.
- [14] Szasz O., Summation of slowly convergent series, Jour. Math. Phys., 28(4) (1950), 272-279.
- [15] Tripathy B.C., Sen M., A note on rate of convergence of sequences den-sity of subsets of natural numbers, Italian Jour. Pure Appl. Math., 17(2005), 151-158.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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