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Keywords:
lacunary sequence; modulus function; statistical convergence; Banach space
lacunary sequence; modulus function; statistical convergence; Banach space
Summary:
The definition of lacunary strong convergence is extended to a definition of lacunary strong convergence with respect to a sequence of modulus functions in a Banach space. We study some connections between lacunary statistical convergence and lacunary strong convergence with respect to a sequence of modulus functions in a Banach space.
References:
[1] Connor J.S.: The statistical and strong $p$-Cesàro convergence of sequences. Analysis 8 (1988), 47-63. MR 0954458 | Zbl 0653.40001
[2] Connor J.S.: On strong matrix summability with respect to a modulus and statistical convergence. Canad. Math. Bull. 32 (1989), 194-198. MR 1006746 | Zbl 0693.40007
[3] Fast H.: Sur la convergence statistique. Colloq. Math. 2 (1951), 241-244. MR 0048548 | Zbl 0044.33605
[4] Freedman A.R., Sember J.J., Raphael M.: Some Cesàro-type summability spaces. Proc. London Math. Soc. 37 (3) (1978), 508-520. MR 0512023 | Zbl 0424.40008
[5] Freedman A.R.. Sember J.J.: Densities and summability. Pacific J. Math. 95 (2) (1981), 293-305. MR 0632187
[6] Fridy J.A., Orhan C.: Lacunary statistical summability. J. Math. Anal. Appl. 173 (1993), 497-504. MR 1209334 | Zbl 0786.40004
[7] Fridy J.A., Orhan C.: Lacunary statistical convergence. Pacific J. Math. 160 (1993), 45-51. MR 1227502 | Zbl 0794.60012
[8] Kolk E.: The statistical convergence in Banach spaces. Acta Comm. Univ. Tartuensis 928 (1991), 41-52. MR 1150232
[9] Lorentz G.G.: A contribution to the theory of divergent sequences. Acta Math. 80 (1948), 167-190. MR 0027868 | Zbl 0031.29501
[10] Maddox I.J.: A new type of convergence. Math. Proc. Camb. Philos. Soc. 83 (1978), 61-64. MR 0493034 | Zbl 0392.40001
[11] Maddox I.J.: Sequence spaces defined by a modulus. Math. Proc. Camb. Philos. Soc. 100 (1986), 161-166. MR 0838663 | Zbl 0631.46010
[12] Maddox I.J.: Inclusion between $FK$ spaces and Kuttner's theorem. Math. Proc. Camb. Philos. Soc. 101 (1987), 523-527. MR 0878899
[13] Nakano H.: Concave modulars. J. Math. Soc. Japan 5 (1953), 29-49. MR 0058882 | Zbl 0050.33402
[14] Niven I., Zuckerman H.S.: An introduction to the theorem of numbers. 4th ed., Wiley, New York, 1980. MR 0572268
[15] Pehlivan S.: Sequence space defined by a modulus function. Erc. Univ. J. Sci. 5 (1989), 875-880.
[16] Pehlivan S., Fisher B.: Some sequence spaces defined by a modulus function. Math. Slovaca 44 (1994), to appear. MR 1361822
[17] Šalát T.: On statistically convergent sequences of real numbers. Math. Slovaca 30 (2) (1980), 139-150. MR 0587239
[18] Schoenberg I.J.: The integrability of certain functions and related summability methods. Amer. Math. Monthly 66 (5) (1959), 361-375. MR 0104946 | Zbl 0089.04002
[19] Ruckle W.H.: $FK$ spaces in which the sequence of coordinate vectors is bounded. Can. J. Math. 25 (1973), 973-978. MR 0338731 | Zbl 0267.46008
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