A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES

In this study, we use generalized difference sequences $\Delta ^{m}x=(\Delta ^{m}x_{k})=(\Delta ^{m-1}x_{k}-\Delta ^{m-1}x_{k+1})$ to obtain more general results about weak convergence and we investigate the concept of $\Delta ^{m} \mathcal{I-}$weak convergence where $m\in \mathbb{N} $. We also define weak $\Delta^{m}\mathcal{I-}$limit points and weak $ \Delta^{m}\mathcal{I-}$cluster points.

Keywords:

Weak convergence, $\mathcal{I}-$convergence, $\Delta ^{m}$ sequences $\mathcal{I}-$limit points, $\mathcal{I}-$cluster points.,

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[1] C. Aydin and F. Basar, Some new difference sequence spaces, Appl. Math.Comput., 157(3) (2004), 677-693.
[2] M. Basarir, On the $\Delta$ statistical convergence of sequences, Firat Uni., Jour. of Science and Engineering, 7(2) (1995), 1-6.
[3] C .A. Bektas, M. Et and R. Colak, Generalized difference sequence spaces and their dual spaces, J.Math.Anal.Appl. 292 (2004), 423-432.
[4] V. K. Bhardwaj and I. Bala, On weak statistical convergence, International Journal of Mathematics and Math. Sci., Vol. 2007, Article ID:38530, doi:10.1155/2007/38530 (2007).9 pages.
[5] J. Connor, M. Ganichev and V. Kadets, A characterization of Banach spaces with seperable duals via weak statistical convergence, J. Math. Anal. Appl. 244 (2000).251-261.
[6] K. Demirci, $\mathcal{I}$ limit superior and limit inferior, Math. Commun. 6 (2001), 165 172.
[7] K. Dems, On I-Cauchy sequence, Real Anal. Exchange 30 (2004/2005), 123 128.
[8] E. Dundar, C. Cakan, Rough I-Convergence, Demonstratio Mathematica, 47(3)(2014), 638-651.
[9] M. Et, On some difference sequence spaces, Doga-Tr. J.of Mathematics 17 (1993), 18-24.
[10] M. Et and R. Colak, On some generalized dierence sequence spaces, Soochow Journal Of Mathematics, 21(4) (1995), 377-386.
[11] M. Et and M. Basarir, On some new generalized difference sequence spaces, Periodica Mathematica Hungarica 35 (3) (1997), 169-175.
[12] M. Et and F. Nuray, $\Delta^m$ Statistical convergence, Indian J.Pure Appl. Math. 32(6) (2001), 961-969.
[13] M. Et. and A. Esi, On Kothe- Toeplitz duals of generalized difference sequence spaces, Malaysian Math. Sci. Soc. 23 (2000), 25-32.
[14] H. Fast, Sur la Convergence Statistique, Coll. Math. 2 (1951), 241-244.
[15] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301-313.
[16] J. A. Fridy. and C. Orhan, Lacunary statistical convergence, Pac. J. Math.160 (1993), 43-51.
[17] H. Gumus and F. Nuray, $\Delta^m$Ideal Convergence, Selcuk J. Appl. Math.12(2) (2011), 101-110.
[18] H. Gumus, Lacunary Weak $\mathcal{I}-$Statistical Convergence, Gen. Math. Notes 28(1) (2015), 50-58.
[19] H. Kizmaz, On certain sequence spaces, Canad. Math. Bull. 24(2) (1981), 169-176.
[20] P. Kostyrko, M. Macaj, T. Salat, T. and M. Sleziak,M., $\mathcal{I}-$convergence and extremal $|mathcal{I}-$limit points, Math. Slovaca 55 (2005), 443-464.
[21] P. Kostyrko, T. Salat and W. Wilezynski, $\mathcal{I}-$convergence, Real Anal. Exchange, 26, 2 (2000), 669-686.
[22] A. Nabiev, S. Pehlivan, M. Gurdal, On I-Cauchy sequence, Taiwanese J. Math. 11 (2) (2007), 569 576.
[23] F. Nuray, Lacunary weak statistical convergence, Math. Bohemica, 136(3) (2011), 259-268.
[24] S. Pehlivan and T. Karaev, Some results related with statistical convergence and Berezin symbols, Jour. of Math. analysis and Appl. V 299(2) (2004), 333-340.
[25] E. Savas $\Delta^m$-strongly summable sequences spaces in 2-normed spaces de ned by ideal convergence and an Orlicz function, Applied Mathematics and Computation 217(1) (2010), 271-276.
[26] E. Savas and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), 826-830.
[27] O. Talo, E. Dundar, $\mathcal{I}-$-Limit Superior and $\mathcal{I}-$-Limit Inferior for Sequences of Fuzzy Numbers, Konuralp Journal of Mathematics, 4(2) (2016), 1643 172.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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