On some new sequence spaces and statistical convergence methods for double sequences

• Autorzy: Belen C. , Yildirim M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences. We also present some inclusion theorems for our newly defined sequence spaces and statistical convergence methods.

Słowa kluczowe

EN

statistical convergence; double sequence; lacunary sequence; Orlicz function

PL

zbieżność statystyczna; sekwencja podwójna; funkcja Orlicza

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 3
• Strony: 627--637
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Belen C.

• Department of Mathematics, Education Ordu, University Ordu, Turkey

autor

Yildirim M.

• Department of Mathematics, Faculty of Science, Cumhuriyet University Sivas, Turkey

Bibliografia

• [1] M. Başarir, On some new sequence spaces, Riv. Mat. Univ. Parma (5) 1 (1992), 339–347.
• [2] T. A. Chishti, Some spaces of lacunary convergent sequences defined by Orlicz functions, Novi Sad J. Math. 35(2) (2005), 19–25.
• [3] R. Çolak, M. Et, E. Malkowsky, Strongly almost (ω, λ)-summable sequences defined by Orlicz functions, Hokkaido Math. J. 34 (2005), 265–276.
• [4] G. Das, S. K. Sahoo, On some sequence spaces, J. Math. Anal. Appl. 164 (1992), 381–398.
• [5] A. Esi, Some new sequence space defined by modulus function and strongly almost statistical convergence, J. Indian Math. Soc. 66 (1999), 81–87.
• [6] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.
• [7] J. A. Fridy, C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160(1) (1993), 43–51.
• [8] M. A. Krasnoselskii, Y. B. Rutisky, Convex Function and Orlicz Spaces, 1961, Groningen, Netherlands.
• [9] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190.
• [10] F. Moricz, B. E. Rhoades, Almost convrgence of double sequences and strong regularity of summability matrices, Math. Proc. Cambridge Philos Soc. 104 (1988), 283–294.
• [11] M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223–231.
• [12] M. Mursaleen, S. A. Mohiuddine, Banach limit and some new spaces of double sequences, Turkish J. Math. 35 (2011), 1–10.
• [13] S. D. Parashar, B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math. 25(4) (1994), 419–428.
• [14] R. F. Patterson, E. Savas, Lacunary statistical convergence of double sequences, Math. Commun. 10 (2005), 55–61.
• [15] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53 (1900), 289–321.
• [16] W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 973–978.
• [17] E. Savas, R. F. Patterson, On some double almost lacunary sequence spaces defined by Orlicz functions, Filomat 19 (2005), 35–44.
• [18] E. Savaş, R. F. Patterson, Some ơ-double sequence spaces defined by Orlicz function, J. Math. Anal. Appl. 324 (2006), 525–531.
• [19] E. Savaş, R. F. Patterson, Lacunary statistical convergence of multiple sequences, Appl. Math. Lett. 19 (2006), 527–534.
• [20] E. Savaş, R. F. Patterson, Double sequence spaces defined by Orlicz functions, Iran. J. Sci. Technol. Trans. A Sci. 31 (2007), 183–188.