On Wijsman I₂-lacunary statistical convergence for double set sequences

• Autorzy: Kіşі Ö.

Identyfikatory

DOI

10.1515/fascmath-2016-0018

• Języki publikacji: EN

Abstrakty

EN

The aim of present work is to present some inclusion relations between the concepts of Wijsman I₂-lacunary statistical convergence and Wijsman strongly I₂-lacunary convergence for double sequences of sets. Also we study the concepts of Wijsman I₂-lacunary statistical convergence, Wijsman I₂- lacunary statistical convergence double sequences of sets and investigate the relationship among them.

Słowa kluczowe

EN

I-convergence; lacunary; double sequences

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2016
• Tom: Nr 57
• Strony: 91--104
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Kіşі Ö.

• Faculty of Science, Mathematics Depertmant, Bartin University Bartin, Turkey

Bibliografia

• [1] Altay B., Başar F., Some new spaces of double sequences, J. Math Anal. Appl., 309(1)(2005), 70-90.
• [2] Baronti M., Papini P., Convergence of sequences of sets. In methods of functional analysis in approximation theory., ISNM 76, Birkhauser, Basel (1986), 133-155.
• [3] Beer G., On convergence of closed sets in a metric space and distance functions, Bull. Austral. Math. Soc., 31(1985), 421-432.
• [4] Beer G., Wijsman convergence: A survey, Set-Valued Var. Anal., 2(1994), 77-94.
• [5] Das P., Savaş E., Ghosal Kr., On generalized of certain sum ability methods using ideals, Appl. Math. Letter, 36(2011), 1509-1514.
• [6] Das P., Kostyrko P., Wilczsyki W., Mali P., I and I*-convergence of double sequences, Math. Slovaca, 58(5)(2008), 605-620.
• [7] Fast H., Sur la convergence statistique, Colloq. Math., 2(1951), 241-244.
• [8] Fridy J.A., Orhan C., Lacunary statistical convergence, Pacific Journal of Mathematics, 160(1993), 43-51.
• [9] Hill JD., On perfect summability of double sequences, Bull. Am Math Soc., 46(1940), 327-331.
• [10] Kisi Ö., Nuray F., New convergence de_nitions for sequences of sets, Abstract and Applied Analysis, Volume 2013, Article ID 852796, 6 pages.
• [11] Kisi Ö., Savaş E., Nuray F., On I-asymptotically lacunary statistical equivalence of sequences of sets, (submitted for publication).
• [12] Kisi Ö., Lacunary ideal convergence of double set sequences, Gen. Math. Notes, 29(2)(2015), 36-47.
• [13] Kostyrko P., Šalat T., Wilezynski W., I-convergence, Real Anal. Exchange, 26(2)(2000), 669-686.
• [14] Kumar S., Kumar V., Bhatia S.S., On ideal version of lacunary statistical convergence of double sequences, Gen. Math. Notes, 17(1)(2013) 32-44.
• [15] Limaea B.V., Zeltser M., On the pringsheim convergence of double series, Proc Est Acad. Sci., 58(2009), 108-121.
• [16] Mursaleen M., Edely O.H.H., Statistical convergence of double sequences, J. Math. Anal. Appl., 288(2003), 223-231.
• [17] Nuray F., Rhoades B.E., Statistical convergence of sequences of sets, Fasc. Math., 49(2012), 87-99.
• [18] Nuray F., Dundar E., Ulusu U., Wijsman I2-convergence of double sequences of closed sets, Pure and Applied Mathematics Letters, 2(2014), 31-35.
• [19] Nuray F., Ulusu U., Dundar E., Lacunary statistical convergence of double sequences of sets, (under communication).
• [20] Nuray F., Ulusu U., Dundar E., Cesàro summability of double sequences of sets, Gen. Math. Notes., 25(1), November (2014), 8-18.
• [21] Nuray F., Dundar E., Ulusu U., Wijsman statistical convergence of double sequences of sets, (under communication).
• [22] Nuray F., Ulusu U., Dundar E., Lacunary statistical convergence of double sequences of sets, (under communication).
• [23] Savas E., Patterson R.F., Lacunary statistical convergence of double sequences, Math. Commun., 10(2005), 55-61.
• [24] Schoenberg I.J., The integrability of certain functions and related summability methods, Amer. Math. Monthly., 66(1959), 361-375.
• [25] Sever Y., Ulusu U., Dundar E., On strongly I and I*-lacunary convergence of sequences of sets, (under communication).
• [26] Tripathy B.C., Hazarika B., Choudhary B., Lacunary I-convergent sequences, Kyungpook Math. J., 52(4)(2012), 473-482.
• [27] Tripathy B., Tripathy B.C., On I-convergent double sequences, Soochow J. Math., 315(2005), 549-560.
• [28] Ulusu U., Nuray F., Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics, 4(2)(2012), 99-109.
• [29] Ulusu U., Nuray F., On strongly lacunary summability of sequence of sets, Journal of Applied Mathematics and Bioinformatics, 3(2013), 75-88.
• [30] Ulusu U., Dundar E., I-lacunary statistical convergence of sequences of sets, Filomat, 28(8)(2014), 1567-1574.
• [31] Ulusu U., Dundar E., Pancaroglu N., Strongly I₂-lacunary convergence and I2-lacunary Cauchy double sequences of sets, International Conference on Recent Advances in Pure and Applied Mathematics.
• [32] Wijsman R.A., Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70(1964), 186-188.
• [33] Wijsman R.A., Convergence of sequences of convex sets, cones and functions II, Trans. Amer. Math. Soc., 123(1)(1966), 32-45.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.