We consider a generalization, under weaker conditions, of the main theorem on quasi-σ-power increasing sequences applied to |A, θn|k summability factors of infinite series and Fourier series. We obtain some new and known results related to the basic summability methods.
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N. K. Bari and S. B. Stechkin, “Best approximation and differential properties of two conjugate functions,” Trudy Mosk. Mat. Obshch., 5, 483–522 (1956).
H. Bor, “On two summability methods,” Math. Proc. Cambridge Philos. Soc., 97, 147–149 (1985).
H. Bor, “On the relative strength of two absolute summability methods,” Proc. Amer. Math. Soc., 113, 1009–1012 (1991).
H. Bor, “A study on weighted mean summability,” Rend. Circ. Mat. Palermo, 56, No. 2, 198–206 (2007).
H. Bor, “On absolute weighted mean summability of infinite series and Fourier series,” Filomat, 30, 2803–2807 (2016).
H. Bor, “Some new results on absolute Riesz summability of infinite series and Fourier series,” Positivity, 20, No. 3, 599–605 (2016).
H. Bor, “An application of power increasing sequences to infinite series and Fourier series,” Filomat, 31, No. 6, 1543–1547 (2017).
E. Cesàro, “Sur la multiplication des sèries,” Bull. Sci. Math., 14, 114–120 (1890).
K. K. Chen, “Functions of bounded variation and the Cesaro means of Fourier series,” Acad. Sinica Sci. Record., 1, 283–289 (1945).
T. M. Flett, “On an extension of absolute summability and some theorems of Littlewood and Paley,” Proc. Lond. Math. Soc. (3), 7, 113–141 (1957).
G. H. Hardy, Divergent Series, Clarendon Press, Oxford (1949).
E. Kogbetliantz, “Sur lès series absolument sommables par la methode des moyennes arithmetiques,” Bull. Sci. Math., 49, 234–256 (1925).
L. Leindler, “A new application of quasi power increasing sequences,” Publ. Math. Debrecen, 58, 791–796 (2001).
H. S. Özarslan and T. Kandefer, “On the relative strength of two absolute summability methods,” J. Comput. Anal. Appl., 11, No. 3, 576–583 (2009).
M. A. Sarıgöl, “On the local properties of factored Fourier series,” Appl. Math. Comput., 216, 3386–3390 (2010).
W. T. Sulaiman, “Inclusion theorems for absolute matrix summability methods of an infinite series. IV,” Indian J. Pure Appl. Math., 34, No. 11, 1547–1557 (2003).
W. T. Sulaiman, “Some new factor theorem for absolute summability,” Demonstr. Math., 46, No. 1, 149–156 (2013).
N. Tanovič-Miller, “On strong summability,” Glas. Mat. Ser. III, 14(34), 87–97 (1979).
¸ S. Yıldız, “A new theorem on absolute matrix summability of Fourier series,” Publ. Inst. Math. (Beograd) (N.S.), 102(116), 107–111 (2017).
¸ S. Yıldız, “On absolute matrix summability factors of infinite series and Fourier series,” Gazi Univ. J. Sci., 30, No. 1, 363–370 (2017).
¸ S. Yıldız, “On the absolute matrix summability factors of Fourier series,” Math. Notes, 103, 297–303 (2018).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 5, pp. 635–643, May, 2020.
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Yıldız, Ş. Matrix Application of Power Increasing Sequences to Infinite Series and Fourier Series. Ukr Math J 72, 730–740 (2020). https://doi.org/10.1007/s11253-020-01813-x
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DOI: https://doi.org/10.1007/s11253-020-01813-x