Lacunary I-convergent σ-asymptotically equivalent difference sequences of fuzzy real numbers

Amar Jyoti Dutta; Sankar Jyoti  Boruah

doi:10.5269/bspm.67390

Amar Jyoti Dutta Institute of Advanced Study in Science and Technology
Sankar Jyoti Boruah Gauhati University

Résumé

In this paper we introduce the concept lacunary (Δ, σ), I-asymptotically equivalent sequences of fuzzy real numbers in terms of Orlicz function, which is a natural combination for the definition of asymptotic equivalent, σ-convergence, difference sequence, Istatistically limit, I-statistically lacunary sequences and Orlicz function of fuzzy real numbers. We have established some relations between the classes of the sequences related to our study.

Téléchargements

Les données sur le téléchargement ne sont pas encore disponible.

Bibliographies de l'auteur

Amar Jyoti Dutta, Institute of Advanced Study in Science and Technology

Mathematical Sciences Division

Research Associate

Sankar Jyoti Boruah, Gauhati University

Department of Mathematics, Gauhati University; Research Scholar

Références

T. Bilgin, (σ, f)-asymptotically lacunary equivalent sequences, Int. Jour. Anal., (2014), doi.org/10.1155/2014/945902

M. Basarir, S. Altunda˘g, On δ-lacunary statistical asymptotically equivalent sequences, Filomat, 22(1), 161-172, (2008).

M. Basarir, S. Altunda˘g, On asymptotically equivalent difference sequences with respect to a modulus function, Riec. Math., 60(2), 299-311, (2011).

A. J. Dutta, Asymptotically equivalent generalized difference sequences of fuzzy real numbers defined by Orlicz function, Thai Jour. Math., 503-515, (2017).

A. Esi, On A-Asymptotically lacunary statistical equivalent sequences, Jour. Appl. Funct. Anal., 5(2), 221-226, (2010).

A. Esi, and A. Esi, On Delta-Asymptotically Equivalent Sequences of Fuzzy Numbers, Inter. Jour. Math. Comp., 1(10), 29-35, (2008).

A. Esi and M.K. ¨ Ozdemir, Asymptotically double lacunary equivalent sequences defined by ideals and Orlicz functions, Research and Reviews: Disc. Math. Struc., 4(2), 7-16, (2017).

M. Et, R. C¸ olak, On some generalized difference sequence spaces, Soochow Jour. Math., 21(4), 377-386, (1995).

B. Hazarika, A. Esi, On fuzzy real valued asymptotically equivalent sequences and lacunary ideal convergence, Annal. Univ. Craiova, Math. Comp. Sc. Series, 41(2), 209-225, (2014).

B. Hazarika, A. Esi, N.L. Braha, On asymptotically Wijsman lacunary σ-statistical convergence of set sequences, Jour. Math. Anal., 4(3), 33-46, (2013).

B. Hazarika and A. Esi, On asymptotically ideal fi-statistical equivalent sequences of fuzzy real numbers, Jour. Ana. Num. Theory, 3(2), 70-88, (2015).

B. Hazarika and A. Esi, On asympotically Wijsman lacunary statistical convergence of set sequences in ideal context, Filomat, 31(9), 2691-2703, (2017).

H. Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24(2), 169-176, (1981).

K. Lindberg, On subspaces of Orlicz sequence spaces, Studia Math., 45, 119-146, (1973).

Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel Jour. Math., 10, 379-390, (1971).

G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80(1), 167-190, (1948).

M. S. Marouf, Asymptotic equivalence and summability, Int. Jour. Math. Math. Sci., 16(4), 755-762, (1993).

F. Nuray, E. Sava¸s, Statistical convergence of sequences of fuzzy numbers, Math. Slovaca, 45(3), 269-273, (1995).

R. F. Patterson, On asymptotically statistical equivalent sequences, Demons. Math., 36(1), 149-154, (2003).

F. Patterson, E. Sava¸s, On asymptotically lacunary statistical equivalent sequences, Thai Jour. Math., 4(2), 267-272, (2012).

E. Sava¸s, On lacunary strong σ-convergence, Indian Jour. Pure Appl. Math., 21(4), 359-365, (1990).

E. Sava¸s, On asymptotically lacunary σ-statistical equivalent sequences of fuzzy numbers, New Math. Natural Comp., 5(3), 589-598, (2009).

E. Sava¸s, On I-asymptotically lacunary statistical equivalent sequences, Adv. Diff. Eq., 1-7, (2013).

R. Sava¸s, M. Ba¸sarir, (σ, δ)-asymptotically statistical equivalent sequences, Filomat, 20(1), 35-42, (2006).

E. Sava¸s, H. Gumu¸s, A generalization on I-asymptotically lacunary statistical equivalent sequences, Jour. Inequal. App., 1-9, (2013).

E. Sava¸s, F. Nuray, On σ-statistically convergence and lacunary σ-statistically convergence, Math. Slovaca, 43(3), 309-315, (1993).

E. Sava¸s, R. F. Patterson, σ-asymptotically lacunary statistical equivalent sequences, Central Euro. Jour. Math., 4(4), 648-655, (2006).

E. Sava¸s, R. F. Patterson, An extension asymptotically lacunary statistical equivalent sequences, The Aligarh Bull. Math., 27(2), 109-113, (2008).

B.C. Tripathy, A. Baruah, M. Et, M. Gungor, On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers, Iran. Jour. Sci. Tech., Transac. A : Sci., 36(2), 147-155, (2012).

B.C. Tripathy, A. Baruah, New type of difference sequence spaces of fuzzy real numbers, Math. Modell. Anal., 14(3), 391-397, (2009).

B.C. Tripathy, A. Baruah: N¨orlund, Riesz mean of sequences of fuzzy real numbers, Appl. Math. Letters, 23, 651-655, (2010).

B.C. Tripathy, A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. Jour., 50(4), 565-574, (2010).

B.C. Tripathy, S. Borgohain, Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function, Adv. Fuzzy Sys., 6, (2011).

B.C. Tripathy, S. Borgohain, The sequence space m(M, ϕ,Δn m, p)F , Math. Model. Anal., 13(4), 577-586, (2008).

B.C. Tripathy, P. Chandra, On some generalized difference paranormed sequence spaces associated with multiplier sequences defined by modulus function, Anal. Theory Appl., 27(1), 21-27, (2011).

B.C. Tripathy, H. Dutta, On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary Δn m-statistical convergence, Anal. Stiin. ale Univ. Ovidius, Seria Matem., 20(1), 417-430, (2012).