c93f955a-6415-40d1-93da-5917e61c9a4720240126060138805wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40511220241220242310.37394/23206.2024.23https://wseas.com/journals/mathematics/2024.phpAntsAasmaDept. of Econ. and Fin., Tallinn Univ. of Technology, Akadeemia tee 3-456, 12618, ESTONIAPinnangudi N.NatarajanOld no. 2/3, new no.3/3 Second main road, R.A.Puram, Chennai 600028, INDIALet α > 1. The α-absolute convergence with speed, where the speed is defined by a monotonically increasing positive sequence µ, has been studied in the present paper. Let l µ α be the set of all α-absolutely µconvergent sequences and X a sequence space defined by another speed λ. Necessary and sufficient conditions for a matrix A (with real or complex entries) to map X into l µ α have been presented. It is proved as an example that the Zweier matrix Z1/2 satisfies these necessary and sufficient conditions for certain speeds λ and µ. The notion of regularity on the subspace X of the set c of converging sequences is defined, and also, necessary and sufficient conditions for a matrix A to be regular on certain X ⊂ c are presented. It has also been shown that there exists an irregular matrix, which is regular on the subspace X of c.1262024126202460677https://wseas.com/journals/mathematics/2024/a145106-005(2024).pdf10.37394/23206.2024.23.7https://wseas.com/journals/mathematics/2024/a145106-005(2024).pdf10.1002/9781119397786A. Aasma, H. Dutta and P. N. Natarajan, An Introductory Course in Summability Theory, John Wiley and Sons, 2017. P. Amore, Convergence acceleration of series through a variational approach, J. Math. Anal. Appl., Vol.323, No.1, 2006, pp. 63-77. 10.1007/978-3-030-58418-4C. Brezinski and M. Redivo-Zaglia, Extrapolation and rational approximation—the works of the main contributors, Springer, 2020. C. Brezinski, Convergence acceleration during the 20th century, J. Comput. Appl. Math., Vol. 122, No.1-2, 2000, pp. 1-21. J.P. Delahaye, Sequence Transformations, Springer, 1988. G. Kangro, Summability factors for the series λ-bounded by the methods of Riesz and Cesa`ro [Množiteli summirujemosti dlya ryadov, -ogranitšennõh metodami Rica i Cezaro], Acta Comment. Univ. Tartu. Math., No. 277, 1971, pp. 136-154. G. Kangro, On the summability factors of the Bohr-Hardy type for a given speed I [O množitelyah summirujemosti tipa Bora-Hardy dlya zadannoi ckorosti I], Proc. Est. Acad. Sci. Phys. Math., Vol.18, No.2, 1969, pp. 137-146. A. Sidi, Practical Extrapolation Methods., Cambridge monographs on applied and computational mathematics 10., Gambridge Univ. Press, 2003. 10.2298/fil2304029aA. Aasma and P. N. Natarajan, Matrix transforms between sequence spaces defined by speeds of convergence, FILOMAT, Vol.37, No.4, 2023, pp. 1029-1036. 10.18514/mmn.2018.2495S. Das and H. Dutta, Characterization of some matrix classes involving some sets with speed, Miskolc Math. Notes, Vol.19, No. 2, 2018, pp. 813–821. 10.1016/0377-0427(94)90059-0I. Kornfeld, Nonexistence of universally accelerating linear summability methods, J. Comput. Appl. Math., Vol.53, No.3, 1994, pp. 309-321. 10.3846/1392-6292.2010.15.103-112A. Sˇeletski and A. Tali, Comparison of speeds of convergence in Riesz-Type families of summability methods II, Math. Model. Anal., Vol. 15, No.1, 2010, pp. 103-112. 10.3176/proc.2008.2.02A. Sˇeletski and A. Tali, Comparison of speeds of convergence in Riesz-Type families of summability methods, Proc. Estonian Acad. Sci. Phys. Math., Vol.57, No.2, 2008, pp. 70-80. U. Stadtmu¨ller and A. Tali, Comparison of certain summability methods by speeds of convergence, Anal. Math., Vol.29, No.3, 2003, pp. 227- 242. 10.3846/1392-6292.2010.15.97-102O. Meronen and I. Tammeraid, Several theorems on λ-summable series, Math. Model. Anal., Vol.15, No.1, 2010, pp. 97–102. I. Tammeraid, Generalized linear methods and convergence acceleration, Math. Model. Anal., Vol.8, No.1, 2003, pp. 87-92. I. Tammeraid, Convergence acceleration and linear methods, Math. Model. Anal., Vol.8, No.4, 2003, pp. 329-335. 10.1016/j.physrep.2007.03.003E. Caliceti, M. Meyer-Hermann, P. Ribeca, A. Surzhykov and U.D. Jentschura, From useful algorithms for slowly convergent series to physical predictions based on divergent perturbativ expansions, Physics Reports-Review Section of Physics Letters, Vol.446, No. 1-3, 2007, pp. 1-96. C. Heissenberg, Convergent and Divergent Series in Physics. A short course by Carl Bender, in: C. Heissenberg (Ed.), Lectures of the 22nd “Saalburg” Summer School, 2016. J. Boos, Classical and Modern Methods in Summability, University Press, 2000. 10.1007/bf01215107M. Stieglitz and H. Tietz, Matrixtransformationen von Folgenra¨umen. Eine Ergebnisu¨bersicht, Math. Z., Vol.154, No.1, 1977, pp. 1-16. S. Baron, Introduction to the theory of summability of series, Valgus, 1977 (in Russian).