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A New Outlook for Almost Convergent Sequence Spaces

Year 2018, Volume: 39 Issue: 1, 34 - 46, 16.03.2018

Murat Candan

https://doi.org/10.17776/csj.383311
Cited By: 1

Abstract



The
point standing out in the present paper is the sequence spaces ,  and produced
by the domain of the infinite matrix ,
which is defined in the previous study of Candan [2], where the spaces ,  and ,
respectively, are as presented by G.G. Lorentz utilizing the issue of the
Banach limits (Acta.  Math.  80. 
1948, 167-190), andis
the double sequential band matrix and G is the generalized weighted mean.
Firstly, it is shown that aforementioned spaces are linearly isomorhic to the
spaces ,  and ,
respectively. In addition to these, andduals
of the spaces  and  are given. Beyond them, the classes  and   of infinite matrices are characterized, where
 is a given sequence space.

Keywords

Almost convergence Generalized weigheted mean Sequence space Matrix transformations

References

  • [1] Choudhary B., Nanda S. Functional Analysis with applications, John Wiley and Sons, (1989), New Delhi, İndia.
  • [2] Candan M., A new sequence space isomorphic to the space ℓ(p) and compact operators, J. Math. Comput. Sci.,4-2 (2014) 306-334.
  • [3] Lorentz G. G. A contribution to the theory of divergent sequences, Acta Mathematica, 80 (1948) 167-190.
  • [4] Kızmaz H. On certain sequence spaces, Canad. Math. Bull. 24-2 (1981) 169-176.
  • [5] Kirişçi M., Almost convergence and generalized weighted mean. AIP Conf. Proc. 1470 (2012) 191-194.
  • [6] Başar F., Kirişçi M. Almost convergence and generalized difference matrix, Comput. Math. Appl.,61 (2011) 602-611.
  • [7] Kayaduman K., Şengönül M. The space of Cesaro almost convergent sequence and core theorems, Acta Math. Scientia,6 (2012) 2265-2278.
  • [8] Candan M. Almost convergence and double sequential band matrix, Acta Math. Scientia, 34-2 (2014): 354-366.
  • [9] Candan M., Kılınç G. A different look for paranormed Riesz sequence space derived by Fibonacci Matrix. Konuralp Journal of Mathematics 3-2 (2015) 62-76.
  • [10] Kirişçi M. Almost convergence and generalized weighted mean II. J. Ineq. and Appl., 1-93 (2014) 13 pages.
  • [11] Polat H., Karakaya V., Şimşek N. Difference sequence space derived by using a generalized weighted mean. Applied Mathematics Letters, 24 (2011) 608-614.
  • [12] Karaisa A., Başar F. Some new paranormed sequence spaces and core theorems. AIP Conf. Proc., 1611 (2014) 380-391.
  • [13] Karaisa A., Özger F. Almost difference sequence spaces derived by using a generalized weighted mean, J. Comput. Anal. and Appl., 19-1 (2015) 27-38.
  • [14] Jarrah A. M., Malkowsky E. BK- spaces, bases and linear operators, Ren. Circ. Mat. Palermo, 52-2 (1990) 177-191.
  • [15] Sıddıqi J. A. Infinite matrices summing every almost periodic sequences, Pacific J. Math., 39-1 (1971) 235-251.
  • [16] Başar F. Summability Theory and Its Applications, Bentham Science Publishers. e-books, Monographs, xi+405 pp., (2012) İstanbul, ISB:978-1-60805-252-3.
  • [17] Duran J. P. Infinite matrices and almost convergence. Math. Z., 128 (1972) 75-83.
  • [18] Öztürk E. On strongly regular dual summability methods, Commun. Fac. Sci. Univ. Ank. Ser. Aâ‚ Math. Stat.,32 (1983) 1-5.
  • [19] King J. P. Almost summable sequences. Proc. Amer. Math. Soc., 17 (1966) 1219-1225.
  • [20] Başar F., Solak İ. Almost-coercive matrix transformations, Rend. Mat. Appl., 11-2 (1991) 249-256.
  • [21] Başar F. f-conservative matrix sequences, Tamkang J. Math., 22-1 (1991) 205-212.
  • [22] Başar F., Çolak R. Almost conservative matrix transformations, Turkish J. Math., 13-3 (1989) 91-100.
  • [23] Başar F. Strongly-conservative sequence to series matrix transformations, Erc.Üni. Fen Bil. Derg., 5-12 (1989) 888-893.
  • [24] Candan M., Kayaduman K. Almost Convergent Sequence Space Derived By Generalized Fibonacci Matrix and Fibonacci Core,British J. Math. Comput. Sci, 7-2 (2015) 150-167.
  • [25] Başarır M., Başar F., Kara E. E. On The Spaces Of Fibonacci Difference Null And Convergent Sequences, arXiv:1309.0150v1 (2013) [math.FA].
  • [26] Kara E. E., Some topological and geometrical properties of new Banach sequences, J. Inequal. Appl., 38 (2013) 15 pp.
  • [27] Candan M. A new aproach on the spaces of generalized Fibonacci difference null and convergent sequences. Math. Aeterna, 1-5 (2015) 191-210.
  • [28] Candan M and Kara E. E., A study on topolojical and geometrical characteristics of new Banach sequence spaces, Gulf J. of Math., 3-4 ( 2015) 67-84.
  • [29] Kara E. E., Başarır M. On compact operators and some Euler- difference sequence spaces, J. Math. Anal. Appl., 379-2 (2011) 499-511.
  • [30] Başarır M., Kara E. E. On some difference sequence spaces of weighted means and compact operators, Ann. Funct. Anal., 2-2 (2011) 114-129.
  • [31] Başarır M., Kara E. E. On the B-difference sequence space derived by generalized weighted mean and compact operators, J. Math. Anal. Appl., 391-1 (2012) 67-81.
  • [32] Kara E. E., İlkhan M. Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64-11 (2016) 2208-2223.
  • [33] Kara E. E., İlkhan M. On Some Banach Sequence Spaces Derived by a New Band Matrix, Br. J. Math. Comput. Sci., 9-2 (2015) 141-159 .
  • [34] Demiriz S., Kara E. E., Başarır M. On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core, Kyungpook Math. J., 55-2 (2015) 355-372.
  • [35] Kara E. E., Demiriz S. Some New Paranormed Difference Sequence Spaces Derived by Fibonacci Numbers, Miskolc Math. Notes, 16-2 (2015) 907-92.
  • [36] Kara E. E., Başarır M., Mursaleen M. Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers”, Kragujevac J. Math., 39-2 (2015) 217-230.
  • [37] Kirişçi M. Reisz type integrated and differentiated sequence spaces, Bulletin of Mathematical Analysis and Applications, 7 (2015) 14-27.
  • [38] Kirişçi M. A note on the some geometric properties of the sequence spaces defined by Taylor method, Far East Journal of Mathematical Sciences (FJMS), 102-7 (2017) 1533-1543.
  • [39] Kirişçi M. Integrated and differentiated spaces of triangular fuzzy numbers", Fasciculi Mathematici, 59 (2017), 75-89.
  • [40] Kirişçi M. Integrated and Differentiated Sequence Spaces, Journal Nonlinear Analysis and Application, (2015 2-16.
  • [41] Kirişçi M. On the Taylor sequence spaces of nonabsolute type which include the spaces and , J. of Math. Analy., 6 (2015) 22-35.
  • [42] Kirişçi M. P-Hahn sequence space", Far East Journal of Mathematical Sciences, 90 (2014) 45-63.
  • [43] Kirişçi M. The Sequence Space bv and Some Applications, Mathematica Aeterna, 4 (2014) 207-223.
  • [44] Kirişçi M. On the spaces of Euler almost bull and Euler almost convergen sequences", Communications, Series A1:Mathematics and Statistics, 62 (2013) 85-100.
  • [45] Ercan S., Bektaş Ç. A. On new Convergent Difference BK-spaces, J. Comput. Anal. Appl., 23-5 (2017) 793-801.
  • [46] Ercan S., Bektaş Ç. A. Some topological and geometric properties of a new BK-space derived by using regular matrix of Fibonacci numbers. Linear Multi linear Algebra, 65-5 (2017) 909-921.
  • [47] Ercan S. and Bektaş Ç. A., The dual spaces of new sequence spaces and their matrix maps. AIP Conference Proceedings, 1798-1 (2017). AIP. Publishing.
  • [48] Ercan S.,Bektaş Ç. A. New properties of BK-spaces defined by using regular matrix of Fibonacci numbers. AIP Conference Proceedings, 1738-1 (2016), AIP. Publishing.
  • [49] Ercan S.,Bektaş Ç. A. On the spaces of bounded and absolutely summable sequences. Facta Univ. Ser. Math. Inform., 32- 3 (2017) 303-318.
  • [50] Et M., Karakaş M., Çınar M. Some Geometric Properties of a New Modular Space, Defined by Zweier Operator, Fixed Point Theory and Applications,165 (2013) 10 pp.
  • [51] Karakaş M., Karabudak H. Lucas Sayıları ve Sonsuz Toeplitz Matrisleri Üzerine Bir Uygulama, Cumhuriyet Sci. J.,38-3 (2017) 557-562.
  • [52] Karakaş M., Karakaş A. M. New Banach Sequence Spaces That Is Defined By the Aid of Lucas Numbers, Iğdır Univ. J. Inst. Sci. & Tech., 7-4 (2017) 103-111.
  • [53] Kılınç G., Candan M. A different approach for almost sequence spaces defined by a generalized weighted mean. SAU, 21-6 (2017) 1529-1536.

Hemen Hemen Yakınsak Dizi Uzaylar için Yeni Bir Bakış

Year 2018, Volume: 39 Issue: 1, 34 - 46, 16.03.2018

Murat Candan

https://doi.org/10.17776/csj.383311
Cited By: 1

Abstract



Banach limiti (Acta.  Math.  80. 
1948, 167-190) kavramını kullanarak G.G. Lorentz hemen hemen
yakınsak dizilerin  uzayını tanımladı. Bu çalışmada öne çıkan
nokta ,  ve  uzaylarının 
Candan [2] tarafından tanımlanan  matris etki alanında olan ,  ve  uzaylarını tanımlamaktır. Burada ikili
dizisel band matrisi de
genelleştirilmiş ağırlıklı ortalamayı göstermektedir. Çalışmada öncelikle ,  ve uzaylarının
sırası ile ,  ve uzaylarına
lineer izomorf oldukları gösterildikten sonra  ve uzaylarının
sırası ile vedualleri
elde edilmiştir. Son bölümde de verilen
herhangi bir dizi uzayı olmak üzere  ve matris sınıflarının karekterizasyonu
verilmiştir.

Keywords

Hemen hemen yakınsaklık Genelleştirilmiş ağırlıklı ortalama Dizi uzayı Matris Dönüşümleri

References

  • [1] Choudhary B., Nanda S. Functional Analysis with applications, John Wiley and Sons, (1989), New Delhi, İndia.
  • [2] Candan M., A new sequence space isomorphic to the space ℓ(p) and compact operators, J. Math. Comput. Sci.,4-2 (2014) 306-334.
  • [3] Lorentz G. G. A contribution to the theory of divergent sequences, Acta Mathematica, 80 (1948) 167-190.
  • [4] Kızmaz H. On certain sequence spaces, Canad. Math. Bull. 24-2 (1981) 169-176.
  • [5] Kirişçi M., Almost convergence and generalized weighted mean. AIP Conf. Proc. 1470 (2012) 191-194.
  • [6] Başar F., Kirişçi M. Almost convergence and generalized difference matrix, Comput. Math. Appl.,61 (2011) 602-611.
  • [7] Kayaduman K., Şengönül M. The space of Cesaro almost convergent sequence and core theorems, Acta Math. Scientia,6 (2012) 2265-2278.
  • [8] Candan M. Almost convergence and double sequential band matrix, Acta Math. Scientia, 34-2 (2014): 354-366.
  • [9] Candan M., Kılınç G. A different look for paranormed Riesz sequence space derived by Fibonacci Matrix. Konuralp Journal of Mathematics 3-2 (2015) 62-76.
  • [10] Kirişçi M. Almost convergence and generalized weighted mean II. J. Ineq. and Appl., 1-93 (2014) 13 pages.
  • [11] Polat H., Karakaya V., Şimşek N. Difference sequence space derived by using a generalized weighted mean. Applied Mathematics Letters, 24 (2011) 608-614.
  • [12] Karaisa A., Başar F. Some new paranormed sequence spaces and core theorems. AIP Conf. Proc., 1611 (2014) 380-391.
  • [13] Karaisa A., Özger F. Almost difference sequence spaces derived by using a generalized weighted mean, J. Comput. Anal. and Appl., 19-1 (2015) 27-38.
  • [14] Jarrah A. M., Malkowsky E. BK- spaces, bases and linear operators, Ren. Circ. Mat. Palermo, 52-2 (1990) 177-191.
  • [15] Sıddıqi J. A. Infinite matrices summing every almost periodic sequences, Pacific J. Math., 39-1 (1971) 235-251.
  • [16] Başar F. Summability Theory and Its Applications, Bentham Science Publishers. e-books, Monographs, xi+405 pp., (2012) İstanbul, ISB:978-1-60805-252-3.
  • [17] Duran J. P. Infinite matrices and almost convergence. Math. Z., 128 (1972) 75-83.
  • [18] Öztürk E. On strongly regular dual summability methods, Commun. Fac. Sci. Univ. Ank. Ser. Aâ‚ Math. Stat.,32 (1983) 1-5.
  • [19] King J. P. Almost summable sequences. Proc. Amer. Math. Soc., 17 (1966) 1219-1225.
  • [20] Başar F., Solak İ. Almost-coercive matrix transformations, Rend. Mat. Appl., 11-2 (1991) 249-256.
  • [21] Başar F. f-conservative matrix sequences, Tamkang J. Math., 22-1 (1991) 205-212.
  • [22] Başar F., Çolak R. Almost conservative matrix transformations, Turkish J. Math., 13-3 (1989) 91-100.
  • [23] Başar F. Strongly-conservative sequence to series matrix transformations, Erc.Üni. Fen Bil. Derg., 5-12 (1989) 888-893.
  • [24] Candan M., Kayaduman K. Almost Convergent Sequence Space Derived By Generalized Fibonacci Matrix and Fibonacci Core,British J. Math. Comput. Sci, 7-2 (2015) 150-167.
  • [25] Başarır M., Başar F., Kara E. E. On The Spaces Of Fibonacci Difference Null And Convergent Sequences, arXiv:1309.0150v1 (2013) [math.FA].
  • [26] Kara E. E., Some topological and geometrical properties of new Banach sequences, J. Inequal. Appl., 38 (2013) 15 pp.
  • [27] Candan M. A new aproach on the spaces of generalized Fibonacci difference null and convergent sequences. Math. Aeterna, 1-5 (2015) 191-210.
  • [28] Candan M and Kara E. E., A study on topolojical and geometrical characteristics of new Banach sequence spaces, Gulf J. of Math., 3-4 ( 2015) 67-84.
  • [29] Kara E. E., Başarır M. On compact operators and some Euler- difference sequence spaces, J. Math. Anal. Appl., 379-2 (2011) 499-511.
  • [30] Başarır M., Kara E. E. On some difference sequence spaces of weighted means and compact operators, Ann. Funct. Anal., 2-2 (2011) 114-129.
  • [31] Başarır M., Kara E. E. On the B-difference sequence space derived by generalized weighted mean and compact operators, J. Math. Anal. Appl., 391-1 (2012) 67-81.
  • [32] Kara E. E., İlkhan M. Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64-11 (2016) 2208-2223.
  • [33] Kara E. E., İlkhan M. On Some Banach Sequence Spaces Derived by a New Band Matrix, Br. J. Math. Comput. Sci., 9-2 (2015) 141-159 .
  • [34] Demiriz S., Kara E. E., Başarır M. On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core, Kyungpook Math. J., 55-2 (2015) 355-372.
  • [35] Kara E. E., Demiriz S. Some New Paranormed Difference Sequence Spaces Derived by Fibonacci Numbers, Miskolc Math. Notes, 16-2 (2015) 907-92.
  • [36] Kara E. E., Başarır M., Mursaleen M. Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers”, Kragujevac J. Math., 39-2 (2015) 217-230.
  • [37] Kirişçi M. Reisz type integrated and differentiated sequence spaces, Bulletin of Mathematical Analysis and Applications, 7 (2015) 14-27.
  • [38] Kirişçi M. A note on the some geometric properties of the sequence spaces defined by Taylor method, Far East Journal of Mathematical Sciences (FJMS), 102-7 (2017) 1533-1543.
  • [39] Kirişçi M. Integrated and differentiated spaces of triangular fuzzy numbers", Fasciculi Mathematici, 59 (2017), 75-89.
  • [40] Kirişçi M. Integrated and Differentiated Sequence Spaces, Journal Nonlinear Analysis and Application, (2015 2-16.
  • [41] Kirişçi M. On the Taylor sequence spaces of nonabsolute type which include the spaces and , J. of Math. Analy., 6 (2015) 22-35.
  • [42] Kirişçi M. P-Hahn sequence space", Far East Journal of Mathematical Sciences, 90 (2014) 45-63.
  • [43] Kirişçi M. The Sequence Space bv and Some Applications, Mathematica Aeterna, 4 (2014) 207-223.
  • [44] Kirişçi M. On the spaces of Euler almost bull and Euler almost convergen sequences", Communications, Series A1:Mathematics and Statistics, 62 (2013) 85-100.
  • [45] Ercan S., Bektaş Ç. A. On new Convergent Difference BK-spaces, J. Comput. Anal. Appl., 23-5 (2017) 793-801.
  • [46] Ercan S., Bektaş Ç. A. Some topological and geometric properties of a new BK-space derived by using regular matrix of Fibonacci numbers. Linear Multi linear Algebra, 65-5 (2017) 909-921.
  • [47] Ercan S. and Bektaş Ç. A., The dual spaces of new sequence spaces and their matrix maps. AIP Conference Proceedings, 1798-1 (2017). AIP. Publishing.
  • [48] Ercan S.,Bektaş Ç. A. New properties of BK-spaces defined by using regular matrix of Fibonacci numbers. AIP Conference Proceedings, 1738-1 (2016), AIP. Publishing.
  • [49] Ercan S.,Bektaş Ç. A. On the spaces of bounded and absolutely summable sequences. Facta Univ. Ser. Math. Inform., 32- 3 (2017) 303-318.
  • [50] Et M., Karakaş M., Çınar M. Some Geometric Properties of a New Modular Space, Defined by Zweier Operator, Fixed Point Theory and Applications,165 (2013) 10 pp.
  • [51] Karakaş M., Karabudak H. Lucas Sayıları ve Sonsuz Toeplitz Matrisleri Üzerine Bir Uygulama, Cumhuriyet Sci. J.,38-3 (2017) 557-562.
  • [52] Karakaş M., Karakaş A. M. New Banach Sequence Spaces That Is Defined By the Aid of Lucas Numbers, Iğdır Univ. J. Inst. Sci. & Tech., 7-4 (2017) 103-111.
  • [53] Kılınç G., Candan M. A different approach for almost sequence spaces defined by a generalized weighted mean. SAU, 21-6 (2017) 1529-1536.
There are 53 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Murat Candan

Publication Date March 16, 2018
Submission Date January 24, 2018
Acceptance Date February 27, 2018
Published in Issue Year 2018Volume: 39 Issue: 1

Cite

APA Candan, M. (2018). A New Outlook for Almost Convergent Sequence Spaces. Cumhuriyet Science Journal, 39(1), 34-46. https://doi.org/10.17776/csj.383311

Cited By

On A New Almost Convergent Sequence Space Defined By The Matrix ∆_u^λ
Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Gülsen KILINÇ
https://doi.org/10.17714/gumusfenbil.639476
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