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Article

Keywords:
FK; AK spaces; paranorm; modulus functions; almost convergence; statistical convergence; de la Vallée–Poussin means
Summary:
The main object of this paper is to introduce and study some sequence spaces which arise from the notation of generalized de la Vallée–Poussin means and the concept of a modulus function.
References:
[1] P. Erdös, Tenenbaum: Sur les densities des certaines suites d’entiers. Proc. London Math. Soc (3), 59, (1989), 417–438 MR 1014865
[2] H. Fast: Sur la convergence statistique. Colloq. Math. 2, (1951), 241–244 MR 0048548 | Zbl 0044.33605
[3] I. J. Maddox: On Kuttner’s theorem. J. London Math. Soc. 43, (1968), 285–290 MR 0225044 | Zbl 0155.38802
[4] I. J. Maddox: On strong almost convergence. Math. Proc. Camb. Phil. Soc. 85, (1979), 345–350 MR 0516094 | Zbl 0417.40007
[5] I. J. Maddox: Sequence spaces defined by a modulus. Math. Proc. Camb. Phil. Soc., 100, (1986), 161–166 MR 0838663 | Zbl 0631.46010
[6] I. J. Maddox: Inclusions between FK–spaces and Kuttner’s theorem. Math. Proc. Camb. Phil. Soc., 101, (1987), 523–527 MR 0878899 | Zbl 0631.46009
[7] Nakano H.: Concave modulus. J. Math. Soc. Japon. 5, (1953), 29-49. MR 0058882
[8] W. H. Ruckle: FK spaces in which the sequence of coordinate vectors is bounded. Canad. J. Math., 25, (1973), 973–978 MR 0338731 | Zbl 0267.46008
[9] E. Savas: On some generalized sequence spaces defined by a modulus. Indian J. Pure appl. Math., 30(5), (1999), 459–464 MR 1694693 | Zbl 0928.40006
[10] E. Savas: Strong almost convergence and almost $\lambda $–statistical convergence. Hokkaido J. Math. (to appear) MR 1795490 | Zbl 0963.40001
[11] A. Wilansky: Functional Analysis. Blaisdell Publishing Company, 1964 MR 0170186 | Zbl 0136.10603
[12] A. Wilansky: Summability through Functional Analysis. North–Holland Mathematical Studies 85, 1984 MR 0738632 | Zbl 0531.40008
[13] A. Zygmund: Trigonometric Series. Second Edition, Cambridge University Press (1979)
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