On Necessary and Sufficient Conditions for Absolute Matrix Summability
Abstract
This study gets a new general theorem related to necessary and sufficient conditions for $\varphi-{\mid D,\beta;\delta\mid}_{k}$ summability of the series $\sum a_n \lambda_n$ whenever the series $\sum a_n$ is summable $\varphi-{\mid C,\beta;\delta\mid}$, where $C=(c_{nv})$ and $D=(d_{nv})$ are two positive normal matrices, $k\geq 1$, $\delta\geq 0$ and $-\beta(\delta{k}+k-1)+k > 0$.
References
H. Bor, Factors for absolute weighted arithmetic mean summability of infinite series, Int. J. Anal. Appl. 14(2) (2017), 175-179. https://doi.org/10.2298/fil1715963b
H. Bor, On some new results for non-decreasing sequences, Tbilisi Math. J. 10(2) (2017), 57-64. https://doi.org/10.1515/tmj-2017-0025
H. Bor, A new note on absolute weighted arithmetic mean summability, Lobachevskii J. Math. 39(2) (2018), 169-172. https://doi.org/10.1134/s1995080218020051
H. Bor and R. P. Agarwal, A new application of almost increasing sequences to factored infinite series, Anal. Math. Phys. 10(3) (2020), Paper No. 26, 7 pp. https://doi.org/10.1007/s13324-020-00369-0
S. Sonker and A. Munjal, On generalized absolute Riesz summability factor of infinite series, Kyungpook Math. J. 58(1) (2018), 37-46. https://doi.org/10.12988/ijma.2016.6690
A. Karakaş, A new application of almost increasing sequences, Ann. Univ. Paedagog. Crac. Stud. Math. 18 (2019), 59-65.
B. Kartal, A theorem on absolute summability of infinite series, Cumhuriyet Sci. J. 40(3) (2019), 563-569. https://doi.org/10.17776/csj.537767
A. Karakaş, On absolute matrix summability factors of infinite series, J. Class. Anal. 13(2) (2018), 133-139. https://doi.org/10.7153/jca-2018-13-09
B. Kartal, On an extension of absolute summability, Konuralp J. Math. 7(2) (2019), 433-437.
B. Kartal, Factors for generalized matrix summability, Erc. Unv. J. Inst. Sci and Tech. 37(3) (2021), 462-467.
H. S. Özarslan, An application of absolute matrix summability using almost increasing and 8-quasi-monotone sequences, Kyungpook Math. J. 59(2) (2019), 233-240.
H. S. Özarslan, A new factor theorem for absolute matrix summability, Quaest. Math. 42(6) (2019), 803-809. https://doi.org/10.2989/16073606.2018.1498407
H. S. Özarslan, Generalized almost increasing sequences, Lobachevskii J. Math. 42(1) (2021), 167-172. https://doi.org/10.1134/S1995080221010212
H. S. Özarslan and B. Kartal, Absolute matrix summability via almost increasing sequence, Quaest. Math. 43(10) (2020), 1477-1485. https://doi.org/10.2989/16073606.2019.1634651
H. S. Özarslan and M.Ö. Şakar, A new application of $(phi, delta)$ monotone sequences, Russ. Math. 3 (2022), 38-43.
H. S. Özarslan and T. Kandefer, On the relative strength of two absolute summability methods, J. Comput. Anal. Appl. 11(3) (2009), 576-583.
H. S. Özarslan and T. Ari, Absolute matrix summability methods, Appl. Math. Lett. 24(12) (2011), 2102-2106. https://doi.org/10.1016/j.aml.2011.06.006
H. S. Özarslan and H. N. Özgen, Necessary conditions for absolute matrix summability methods, Boll. Unione Mat. Ital. 8(3) (2015), 223-228. https://doi.org/10.1007/s40574-015-0039-8
H. N. Özgen, On two absolute matrix summability methods, Boll. Unione Mat. Ital. 9(3) (2016), 391-397. https://doi.org/10.1007/s40574-016-0053-5
S. A. Sezer and İ. Çanak, Conditions for the equivalence of power series and discrete power series methods of summability, Filomat 29(10) (2015), 2275-2280. https://doi.org/10.2298/fil1510275s
H. Bor, Some equivalence theorems on absolute summability methods, Acta Math. Hungar. 149(1) (2016), 208-214. https://doi.org/10.1007/s10474-016-0582-5
R. G. Cooke, Infinite Matrices and Sequence Spaces, Macmillan & Co. Limited, London, 1950.
I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, Cambridge, 1970.
H. S. Özarslan and B. Kartal, On the general method of summability, J. Math. Anal., 9(4) (2018), 36-43.
N. Tanovic-Miller, On strong summability, Glasnik Mat. Ser. III 14(34) (1979), 87-97.
H. S. Özarslan and T. Ari, A new note on generalized absolute matrix summability, J. Inequal. Appl. 166 (2012), 9 pp. https://doi.org/10.1186/1029-242x-2012-166
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