Genelleştirilmiş ağırlıklı B-Fark ortalama metoduyla tanımlanan hemen hemen yakınsak dizi uzayları için farklı bir yaklaşım
Yıl 2017,
Cilt: 21 Sayı: 6, 1529 - 1536, 01.12.2017
Gülsen Kılınç
,
Murat Candan
Öz
Bu çalışmada, B-fark matrisi ile genelleştirilmiş ağırlıklı ortalama metodu
yardımıyla inşa edilen ve dizi
uzaylarını tanımlandı. Bu uzaylar, genelleştirilmiş ağırlıklı -fark ortalamaları sırasıyla ve uzaylarında olan dizilerin uzayıdır. ve uzaylarının - ve -dualleri elde edildi. Ayrıca, herhangi bir dizi uzayı olmak üzere ve sonsuz matrisleri karakterize edildi.
Kaynakça
- [1] B. Choudhary and S. Nanda, “Functional Analysis with applications,” John Wiley and Sons, New Delhi, I ̇ndia, 1989.
- [2] G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Mathematica, vol. 80, pp. 167-190, 1948.
- [3] H. Kızmaz, “On certain sequence spaces,” Canad. Math. Bull. Vol.24, no.2, pp.169-176, 1981.
- [4] M. Kirisçi, “Almost convergence and generalized weighted mean,” AIP Conf. Proc, vol. 1470, pp. 191–194, 2012.
- [5] F. Başar and M. Kirisçi, “Almost convergence and generalized difference matrix,” Comput. Math. Appl., vol. 11, no. 1, pp. 51–63, 2000.
- [6] K. Kayaduman and M. Şengönül, “On the Riesz almost convergent sequence space,” Abstr. Appl. Anal. Vol. 2012, article ID: 691694, 18 pages.
- [7] M. Candan, “Almost convergence and double sequential band matrix,” Acta Math. Scientia, vol. 34, no. 2, pp. 354–366, 2014.
- [8] D. Butkovic, H. Kraljevic and N. Sarapa “ on the almost convergence,” in Functional analysis, II, Lecture Notes in Mathematics, vol. 1242, 396417,
Springer, Berlin, Germany, 1987.
- [9] M. Kirisçi, “Almost convergence and generalized weighted mean II,” J. Ineq. and Appl, vol.1, no.93, 13 pages, 2014.
- [10] H. Polat, V. Karakaya and N. Şimşek, “Difference sequence space reproduced by using a generalized weighted mean,” Applied Mathematics Letters, vol. 24, pp. 608–614, 2011.
- [11] A. Karaisa and F.Başar, “Some new paranormed sequence spaces and core theorems,” AIP Conf. Proc. Vol. 1611, pp. 380–391, 2014.
- [12] A. Karaisa and F. Özger, “Almost difference sequence spaces reproduced by using a generalized weighted mean,” J. Comput. Anal. and Appl., vol. 19, no. 1, pp. 27–38, 2015.
- [13] K. Kayaduman and M. Şengönül, The space of Cesaro almost convergent sequence and core theorems,” Acta Mathematica Scientia, vol. 6, pp. 2265–2278, 2012.
- [14] A. M. Jarrah and E. Malkowsky, “BK- spaces, bases and linear operators,” Ren. Circ. Mat. Palermo, vol. 2, no. 52, pp. 177–191, 1990.
- [15] J. A. Sıddıqi, “Infinite matrices summing every almost periodic sequences,” Pacific J. Math, vol. 39, no. 1, pp. 235–251, 1971.
- [16] F. Başar, “Summability Theory and Its Applications,” Bentham Science Publishers e-books, Monographs, xi+405 pp, ISB:978-1-60805-252-3, I ̇stanbul, (2012).
- [17] J. P. Duran, “Infinite matrices and almost convergence,” Math. Z. Vol.128, pp.75-83, 1972.
- [18] E. Öztürk, “On strongly regular dual summability methods,” Commun. Fac. Sci. Univ. Ank. Ser. A_1 Math. Stat., vol.32, p. 1-5, 1983.
- [19] J. P. King, “Almost summable sequences,” Proc. Amer. Math. Soc. vol. 17, pp. 1219–1225, 1966.
- [20] F. Basar and İ. Solak, “Almost-coercive matrix transformations,” Rend. Mat. Appl. vol. 7, no.11, pp. 249–256, 1991.
- [21] F. Başar, “f-conservative matrix sequences” Tamkang J. Math, vol. 22, no. 2, pp. 205–212, 1991.
- [22] F. Başar and R. Çolak, “Almost-conserva- tive matrix transformations,” Turkish J. Math, vol. 13, no.3, pp. 91- 100, 1989.
- [23] F. Başar, “Strongly-conservative sequence to series matrix transformations,” Erc. Üni. Fen Bil. Derg. vol. 5, no.12, pp. 888–893, 1989.
- [24] M. Candan and K. Kayaduman, “Almost Convergent sequence space Reproduced By Generalized Fibonacci Matrix and Fibonacci Core,” British J. Math. Comput. Sci, (Yayın No: 2002714), Doi: 10.9734/BJMCS/2015/15923.
- [25] M. Candan, “Domain of Double Sequential Band Matrix in the Spaces of Convergent and Null Sequences,” Advanced in Difference Equations, vol.1, pp. 1-18, Yayın No: 2280631, 2014.
- [26] M. Candan and A. Güneş, “Paranormed sequence spaces of Non Absolute Type Founded Using Generalized Difference Matrix,” Proceedings of the National Academy of Sciences; India Section A: Physical Sciences, vol. 85, no.2, pp. 269- 276, Yayın No:20038692014, Doi: 10.1007/s40010-015-0204-6, 2014.
- [27] M. Candan, “A new Perspective On Paranormed Riesz sequence space of Non Absolute Type,” Global Journal of Mathematical Analysis, vol.3, no. 4, pp. 150–163, Doi: 1
A different approach for almost sequence spaces defined by a generalized weighted means
Yıl 2017,
Cilt: 21 Sayı: 6, 1529 - 1536, 01.12.2017
Gülsen Kılınç
,
Murat Candan
Öz
In this study, we introduce and sequence spaces which consisting of all
the sequences whose generalized weighted -difference means are found
in and spaces utilising generalized weighted mean
and -difference matrices. The -and the -duals of the spaces and are determined. At the same time, we have
characterized the infinite matrices and , where is any given sequence space.
Kaynakça
- [1] B. Choudhary and S. Nanda, “Functional Analysis with applications,” John Wiley and Sons, New Delhi, I ̇ndia, 1989.
- [2] G. G. Lorentz, “A contribution to the theory of divergent sequences,” Acta Mathematica, vol. 80, pp. 167-190, 1948.
- [3] H. Kızmaz, “On certain sequence spaces,” Canad. Math. Bull. Vol.24, no.2, pp.169-176, 1981.
- [4] M. Kirisçi, “Almost convergence and generalized weighted mean,” AIP Conf. Proc, vol. 1470, pp. 191–194, 2012.
- [5] F. Başar and M. Kirisçi, “Almost convergence and generalized difference matrix,” Comput. Math. Appl., vol. 11, no. 1, pp. 51–63, 2000.
- [6] K. Kayaduman and M. Şengönül, “On the Riesz almost convergent sequence space,” Abstr. Appl. Anal. Vol. 2012, article ID: 691694, 18 pages.
- [7] M. Candan, “Almost convergence and double sequential band matrix,” Acta Math. Scientia, vol. 34, no. 2, pp. 354–366, 2014.
- [8] D. Butkovic, H. Kraljevic and N. Sarapa “ on the almost convergence,” in Functional analysis, II, Lecture Notes in Mathematics, vol. 1242, 396417,
Springer, Berlin, Germany, 1987.
- [9] M. Kirisçi, “Almost convergence and generalized weighted mean II,” J. Ineq. and Appl, vol.1, no.93, 13 pages, 2014.
- [10] H. Polat, V. Karakaya and N. Şimşek, “Difference sequence space reproduced by using a generalized weighted mean,” Applied Mathematics Letters, vol. 24, pp. 608–614, 2011.
- [11] A. Karaisa and F.Başar, “Some new paranormed sequence spaces and core theorems,” AIP Conf. Proc. Vol. 1611, pp. 380–391, 2014.
- [12] A. Karaisa and F. Özger, “Almost difference sequence spaces reproduced by using a generalized weighted mean,” J. Comput. Anal. and Appl., vol. 19, no. 1, pp. 27–38, 2015.
- [13] K. Kayaduman and M. Şengönül, The space of Cesaro almost convergent sequence and core theorems,” Acta Mathematica Scientia, vol. 6, pp. 2265–2278, 2012.
- [14] A. M. Jarrah and E. Malkowsky, “BK- spaces, bases and linear operators,” Ren. Circ. Mat. Palermo, vol. 2, no. 52, pp. 177–191, 1990.
- [15] J. A. Sıddıqi, “Infinite matrices summing every almost periodic sequences,” Pacific J. Math, vol. 39, no. 1, pp. 235–251, 1971.
- [16] F. Başar, “Summability Theory and Its Applications,” Bentham Science Publishers e-books, Monographs, xi+405 pp, ISB:978-1-60805-252-3, I ̇stanbul, (2012).
- [17] J. P. Duran, “Infinite matrices and almost convergence,” Math. Z. Vol.128, pp.75-83, 1972.
- [18] E. Öztürk, “On strongly regular dual summability methods,” Commun. Fac. Sci. Univ. Ank. Ser. A_1 Math. Stat., vol.32, p. 1-5, 1983.
- [19] J. P. King, “Almost summable sequences,” Proc. Amer. Math. Soc. vol. 17, pp. 1219–1225, 1966.
- [20] F. Basar and İ. Solak, “Almost-coercive matrix transformations,” Rend. Mat. Appl. vol. 7, no.11, pp. 249–256, 1991.
- [21] F. Başar, “f-conservative matrix sequences” Tamkang J. Math, vol. 22, no. 2, pp. 205–212, 1991.
- [22] F. Başar and R. Çolak, “Almost-conserva- tive matrix transformations,” Turkish J. Math, vol. 13, no.3, pp. 91- 100, 1989.
- [23] F. Başar, “Strongly-conservative sequence to series matrix transformations,” Erc. Üni. Fen Bil. Derg. vol. 5, no.12, pp. 888–893, 1989.
- [24] M. Candan and K. Kayaduman, “Almost Convergent sequence space Reproduced By Generalized Fibonacci Matrix and Fibonacci Core,” British J. Math. Comput. Sci, (Yayın No: 2002714), Doi: 10.9734/BJMCS/2015/15923.
- [25] M. Candan, “Domain of Double Sequential Band Matrix in the Spaces of Convergent and Null Sequences,” Advanced in Difference Equations, vol.1, pp. 1-18, Yayın No: 2280631, 2014.
- [26] M. Candan and A. Güneş, “Paranormed sequence spaces of Non Absolute Type Founded Using Generalized Difference Matrix,” Proceedings of the National Academy of Sciences; India Section A: Physical Sciences, vol. 85, no.2, pp. 269- 276, Yayın No:20038692014, Doi: 10.1007/s40010-015-0204-6, 2014.
- [27] M. Candan, “A new Perspective On Paranormed Riesz sequence space of Non Absolute Type,” Global Journal of Mathematical Analysis, vol.3, no. 4, pp. 150–163, Doi: 1