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

Hafize Gümüş; Mikail Et

Araştırma Makalesi

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

Yıl 2017, Cilt: 5 Sayı: 1, 113 - 122, 01.04.2017

Hafize Gümüş Mikail Et

Öz

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.

Anahtar Kelimeler

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

Kaynakça

[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 dened 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.

Yıl 2017, Cilt: 5 Sayı: 1, 113 - 122, 01.04.2017

Hafize Gümüş Mikail Et

Öz

Kaynakça

[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 dened 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.

Toplam 27 adet kaynakça vardır.

Ayrıntılar

Konular	Mühendislik
Bölüm	Articles
Yazarlar	Hafize Gümüş Bu kişi benim Mikail Et
Yayımlanma Tarihi	1 Nisan 2017
Gönderilme Tarihi	18 Şubat 2017
Kabul Tarihi	25 Ocak 2017
Yayımlandığı Sayı	Yıl 2017 Cilt: 5 Sayı: 1

Kaynak Göster

APA	Gümüş, H., & Et, M. (2017). A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES. Konuralp Journal of Mathematics, 5(1), 113-122.
AMA	Gümüş H, Et M. A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES. Konuralp J. Math. Nisan 2017;5(1):113-122.
Chicago	Gümüş, Hafize, ve Mikail Et. “A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES”. Konuralp Journal of Mathematics 5, sy. 1 (Nisan 2017): 113-22.
EndNote	Gümüş H, Et M (01 Nisan 2017) A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES. Konuralp Journal of Mathematics 5 1 113–122.
IEEE	H. Gümüş ve M. Et, “A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES”, Konuralp J. Math., c. 5, sy. 1, ss. 113–122, 2017.
ISNAD	Gümüş, Hafize - Et, Mikail. “A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES”. Konuralp Journal of Mathematics 5/1 (Nisan 2017), 113-122.
JAMA	Gümüş H, Et M. A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES. Konuralp J. Math. 2017;5:113–122.
MLA	Gümüş, Hafize ve Mikail Et. “A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES”. Konuralp Journal of Mathematics, c. 5, sy. 1, 2017, ss. 113-22.
Vancouver	Gümüş H, Et M. A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES. Konuralp J. Math. 2017;5(1):113-22.

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