A New Variation on Absolute Summability
A New Variation on Absolute Summability
In [4], Bor has proved a main theorem dealing with absolute weighted arithmetic mean summability factors of infinite series by using a positive non-decreasing sequence. In this paper, we have extended this result to absolute matrix summability method by using an almost increasing sequence in place of a positive non-decreasing sequence. Also, some new and known results are also obtained.
___
- [1] N. K. Bari, S. B. Steckin, Best approximation and differential of two conjugate functions, Trudy. Moskov. Mat. Obsc. 5 (1956) 483-522 (in Russian).
- [2] H. Bor, On two summability methods, Math. Proc. Camb. Philos. Soc. 97 (1985) 147-149.
- [3] H. Bor, A note on $\left|\bar{N},p_n\right| _k$ summability factors of in nite series, Indian J. Pure Appl. Math.
18 (1987) 330-336.
- [4] H. Bor, Factors for absolute weighted arithmetic mean summability of in nite series, Int. J.
Anal. Appl. 14 (2017) 175-179.
- [5] H. Bor, An application of quasi-monotone sequences to in nite series and Fourier series,
Anal. Math. Phys. 8 (2018) 7783.
- [6] H. Bor, On absolute summability of factored in nite series and trigonometric Fourier series,
Results Math. 73 (2018) 116.
- [7] H. Bor, On absolute Riesz summability factors of in nite series and their application to
Fourier series, Georgian Math. J. 26 (2019) 361366.
- [8] H. Bor, Certain new factor theorems for in nite series and trigonometric Fourier series,
Quaest. Math. 43 (2020) 441448
- [9] E. Cesaro, Sur la multiplication des series, Bull. Sci. Math. 14 (1890) 114-120.
- [10] T. M. Flett, On an extension of absolute summability and some theorems of Littlewood and
Paley, Proc. Lond. Math. Soc. 7 (1957) 113-141.
- [11] G. H. Hardy, Divergent Series, Clarendon Press. Oxford, (1949).
- [12] K. N. Mishra, On the absolute Norlund summability factors of in nite series, Indian J. Pure
Appl. Math. 14 (1983) 40-43.
- [13] K. N. Mishra and R. S. L. Srivastava, On the absolute Cesaro summability factors of in nite
series, Portugal Math. 42 (1983/84) 53-61.
- [14] K. N. Mishra and R. S. L. Srivastava, On j N ; pnj summability factors of in nite series,
Indian J. Pure Appl. Math. 15 (1984) 651-656.
- [15] H. S. Ozarslan, T. Kandefer, On the relative strength of two absolute summability methods,
J. Comput. Anal. Appl. 11 (2009) 576{583.
- [16] B. E. Rhoades, Inclusion theorems for absolute matrix summability methods, J. Math. Anal.
Appl. 238 (1999) 82-90.
- [17] W. T. Sulaiman, Inclusion theorems for absolute matrix summability methods of an in nite
series, IV. Indian J. Pure Appl. Math. 11 (2003) 1547-1557.
- [18] S. Yıldız, On application of matrix summability to Fourier series, Math. Methods Appl. Sci.
(2018) 664{670.
- [19] S. Yıldız, On the absolute matrix summability factors of Fourier series, Math. Notes 103
(2018) 297-303.
- [20] S. Yıldız, A matrix application on absolute weighted arithmetic mean summability factors
of in nite series, Tibilisi Math. J. 11 (2018) 59-65.
- [21] S. Yıldız, On the generalizations of some factors theorems for in nite series and Fourier
series, Filomat 33 (2019) 4343-4351.
- [22] S. Yıldız, Matrix application of power increasing sequences to in nite series and Fourier
series, Ukranian Math. J. 72 (2020) 730-740.
- [23] S. Yıldız, A variation on absolute weighted mean summability factors of Fourier series and
its conjugate series, Bol. Soc. Parana. Mat. 38 (2020) 105-113.
- [24] S. Yıldız, A recent extension of the weighted mean summability of in nite series, J. Appl.
Math. Inform. 39 (2021) 117-124.