In this paper we define the sequence space $E_{n}^{q}(M,p,s)$ by using an Orlicz function and we study various properties and obtain some inclusion relations involving this space. We give some relations between $N_{k}-$lacunary statistical convergence and strongly $N_{k}-$lacunary convergence.
References
Y. Alt\i n, M. Et and B.C. Tripathy, The sequence space $|\overline{N}\sb p|(M,r,q,s)$ on seminormed spaces, Appl. Math. Comput. 154 (2004), no. 2, 423–430. MR2111379 1072.46006 10.1016/S0096-3003(03)00722-7 Y. Alt\i n, M. Et and B.C. Tripathy, The sequence space $|\overline{N}\sb p|(M,r,q,s)$ on seminormed spaces, Appl. Math. Comput. 154 (2004), no. 2, 423–430. MR2111379 1072.46006 10.1016/S0096-3003(03)00722-7
Y. Altun and T. Bilgin, On a new class of sequences related to the $l_{p}$ space defined by Orlicz function, Taiwanese J. Math. 13 (2009), no. 4, 1189–1196. MR2543736 1190.46006 Y. Altun and T. Bilgin, On a new class of sequences related to the $l_{p}$ space defined by Orlicz function, Taiwanese J. Math. 13 (2009), no. 4, 1189–1196. MR2543736 1190.46006
V.K. Bhardwaj and N. Singh, Some sequence spaces defined by Orlicz functions, Demonstratio Math. 33 (2000), no. 3, 571–582. MR1791722 0966.46002 V.K. Bhardwaj and N. Singh, Some sequence spaces defined by Orlicz functions, Demonstratio Math. 33 (2000), no. 3, 571–582. MR1791722 0966.46002
R. Çolak, B.C. Tripathy and M. Et, Lacunary strongly summable sequences and $q-$lacunary almost statistical convergence, Vietnam J. Math. 34 (2006), no. 2, 129–138. MR2247572 R. Çolak, B.C. Tripathy and M. Et, Lacunary strongly summable sequences and $q-$lacunary almost statistical convergence, Vietnam J. Math. 34 (2006), no. 2, 129–138. MR2247572
N.L. Braha, A new class of sequences related to the $l_{p}$ spaces defined by sequences of Orlicz functions, J. Inequal. Appl. 2011, Article ID 539745, 10 p. (2011). MR2781438 1236.46006 N.L. Braha, A new class of sequences related to the $l_{p}$ spaces defined by sequences of Orlicz functions, J. Inequal. Appl. 2011, Article ID 539745, 10 p. (2011). MR2781438 1236.46006
G. Das and S.K. Mishra, Banach limits and lacunary strong almost convegence, J. Orissa Math. Soc. 2 (1983), 61–70. MR836862 0568.40001 G. Das and S.K. Mishra, Banach limits and lacunary strong almost convegence, J. Orissa Math. Soc. 2 (1983), 61–70. MR836862 0568.40001
M. Et, Y. Altin, Choudhary, B. and B.C. Tripathy, On some classes of sequences defined by sequences of Orlicz functions, Math. Inequal. Appl. 9 (2006), no. 2, 335–342. MR2225019 M. Et, Y. Altin, Choudhary, B. and B.C. Tripathy, On some classes of sequences defined by sequences of Orlicz functions, Math. Inequal. Appl. 9 (2006), no. 2, 335–342. MR2225019
M. Et, A. Gökhan and H. Altinok, On statistical convergence of vector-valued sequences associated with multiplier sequences, Ukrainian Math. J. 58 (2006), no. 1, 139–146 MR2244910 M. Et, A. Gökhan and H. Altinok, On statistical convergence of vector-valued sequences associated with multiplier sequences, Ukrainian Math. J. 58 (2006), no. 1, 139–146 MR2244910
H. Fast, Sur la convergence statistique, Colloquium Math. 2 (1951), 241–244. MR48548 0044.33605 H. Fast, Sur la convergence statistique, Colloquium Math. 2 (1951), 241–244. MR48548 0044.33605
A.R. Freedman, J.J. Sember and M. Raphael, Some Cesaro-type summability spaces, Proc. London Math. Soc. 37 (1978), 508–520. MR512023 10.1112/plms/s3-37.3.508 A.R. Freedman, J.J. Sember and M. Raphael, Some Cesaro-type summability spaces, Proc. London Math. Soc. 37 (1978), 508–520. MR512023 10.1112/plms/s3-37.3.508
J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993), 43–51. MR1227502 0794.60012 10.2140/pjm.1993.160.43 euclid.pjm/1102624563
J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993), 43–51. MR1227502 0794.60012 10.2140/pjm.1993.160.43 euclid.pjm/1102624563
P.K. Kamptan and M. Gupta, Sequence Spaces and Series, Marcel Dekker Inc., New York, 1981. MR606740 0447.46002 P.K. Kamptan and M. Gupta, Sequence Spaces and Series, Marcel Dekker Inc., New York, 1981. MR606740 0447.46002
J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 1 (1971), 379–390. MR313780 10.1007/BF02771656 J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 1 (1971), 379–390. MR313780 10.1007/BF02771656
M. Mursaleen, Q.A. Khan and T.A. Chishti, Some new convergent sequences spaces defined by Orlicz functions and statistical convergence, Ital. J. Pure Appl. Math. 9 (2001), 25–32. MR1842383 M. Mursaleen, Q.A. Khan and T.A. Chishti, Some new convergent sequences spaces defined by Orlicz functions and statistical convergence, Ital. J. Pure Appl. Math. 9 (2001), 25–32. MR1842383
D. Rath and B.C. Tripathy, On statistically convergent and statistically Cauchy sequences, Indian J. Pure. Appl. Math., 25 (1994), no. 4, 381–386. MR1272809 D. Rath and B.C. Tripathy, On statistically convergent and statistically Cauchy sequences, Indian J. Pure. Appl. Math., 25 (1994), no. 4, 381–386. MR1272809
T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150. MR587239 0437.40003 T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150. MR587239 0437.40003
E. Savaş, Strong almost convergence and almost $ \lambda $-statistically convergence, Hokkaido Math. J. 29 (2000), 531-536. MR1795490 0963.40001 E. Savaş, Strong almost convergence and almost $ \lambda $-statistically convergence, Hokkaido Math. J. 29 (2000), 531-536. MR1795490 0963.40001
E. Savas and B.E. Rhoades, On some new sequence spaces of invariant means defined by Orlicz functions, Math. Inequal. Appl. 5 (2002), no. 2, 271–281. MR1899095 E. Savas and B.E. Rhoades, On some new sequence spaces of invariant means defined by Orlicz functions, Math. Inequal. Appl. 5 (2002), no. 2, 271–281. MR1899095
I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375. MR104946 10.2307/2308747 I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375. MR104946 10.2307/2308747
