Bir genelleştirilmiş ağırlıklı ortalama ile tanımlanan hemen hemen yakınsak dizi uzayları için bir farklı yaklaşım
Bu çalışmada, B-fark matrisi ile genelleştirilmiş ağırlıklı ortalama metodu yardımıyla inşa edilen (, ), (, ) ve (, ) dizi uzayları 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.
A different approach for almost sequence spaces defined by a generalized weighted means
In this study, we introduce (, ), (, ) and (, ) sequence spaces which consisting of all the sequences whosegeneralized weighted -difference means are found in , and spaces utilising generalized weighted mean and -differencematrices. The -and the -duals of the spaces (, ) and (, ) are determined. At the same time, we have characterized theinfinite matrices ((, ): ) and (: (, )), where is any given sequence space.
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- B. Choudhary and S. Nanda, “Functional Analysis
with applications,” John Wiley and Sons, New
Delhi, ndia ̇ , 1989
- G. G. Lorentz, “A contribution to the theory of
divergent sequences,” Acta Mathematica, Vol. 80,
pp. 167-190, 1948.
- H. Kızmaz, “On certain sequence spaces,” Canad.
Math. Bull. Vol. 24, no.2, pp.169-176, 1981.
- M. Kirisçi, “Almost convergence and generalized
weighted mean,” AIP Conf. Proc, Vol. 1470, pp.
191–194, 2012.
- F. Başar and M. Kirisçi, “Almost convergence and
generalized difference matrix,” Comput. Math.
Appl., Vol. 61, pp. 602-611, 2011.
- K. Kayaduman and M. Şengönül, “On the Riesz
almost convergent sequence space,” Abstr. Appl.
Anal. Vol. 2012, article ID: 691694, 18 pages, 2012.
- M. Candan, “Almost convergence and double
sequential band matrix,” Acta Math. Scientia, Vol.
34, no. 2, pp. 354–366, 2014.
- 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.
- M. Kirisçi, “Almost convergence and generalized
weighted mean II,” J. Ineq. and Appl, Vol.1, no.93,
13 pages, 2014.
- 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.
- A. Karaisa and F. Başar, “Some new paranormed
sequence spaces and core theorems,” AIP Conf.
Proc. Vol. 1611, pp. 380–391, 2014.
- 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.
- K. Kayaduman and M. Şengönül, “The space of
Cesaro almost convergent sequence and core
theorems,” Acta Mathematica Scientia, Vol. 6, pp.
2265–2278, 2012.
- A. M. Jarrah and E. Malkowsky, “BK- spaces, bases
and linear operators,” Ren. Circ. Mat. Palermo, Vol.
2, no. 52, pp. 177–191, 1990.
- J. A. Sıddıqi, “Infinite matrices summing every
almost periodic sequences,” Pacific J. Math, Vol.
39, no. 1, pp. 235–251, 1971.
- F. Başar, “Summability Theory and Its
Applications,” Bentham Science Publishers ebooks, Monographs, xi+405 pp, ISB:978-1-60805-
252-3, İstanbul, (2012).
- J. P. Duran, “Infinite matrices and almost
convergence,” Math. Z. Vol.128, pp.75-83, 1972.
- E. Öztürk, “On strongly regular dual summability
methods,” Commun. Fac. Sci. Univ. Ank. Ser.
Math. Stat., Vol. 32, p. 1-5, 1983.
- J. P. King, “Almost summable sequences,” Proc.
Amer. Math. Soc. Vol. 17, pp. 1219–1225, 1966.
- F. Basar and İ. Solak, “Almost-coercive matrix
transformations,” Rend. Mat. Appl. Vol. 7, no.11,
pp. 249–256, 1991.
- F. Başar, “-conservative matrix sequences”
Tamkang J. Math, Vol. 22, no. 2, pp. 205–212,
1991.
- F. Başar and R. Çolak, “Almost-conserva- tive
matrix transformations,” Turkish J. Math, Vol. 13,
no.3, pp. 91- 100, 1989.
- F. Başar, “Strongly-conservative sequence to series
matrix transformations,” Erc. Üni. Fen Bil. Derg.
Vol. 5, no.12, pp. 888–893, 1989.
- M. Candan and K. Kayaduman, “Almost
Convergent sequence space Reproduced By
Generalized Fibonacci Matrix and Fibonacci Core,”
British J. Math. Comput. Sci, Vol. 7, no.2, pp.150-
167, 2015.
- 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, 2014.
- 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,
2014.
- 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: 10.14419/gjma.v3i4.5335,
2015.
- E. E. Kara and M. İlkhan, “Some Properties of
Generalized Fibonacci Sequence Spaces,” Linear
and Multilinear Algebra, Vol. 64, no. 11, pp. 2208-
2223, 2016.
- S. Ercan and Ç. A. Bektaş, “On some sequence
spaces of non-absolute type,” Kragujevac J. Math.,
Vol. 38, no. 1, pp. 195-202, 2014.
- S. Ercan and Ç. A. Bektaş, “On new
−Convergent Difference BK-spaces,” J.
Comput. Anal. Appl., Vol. 23, no. 5, pp. 793-801,
2017.
- M. Başarır and E. E. Kara, “On the B-Difference
Sequence Spaces Derived by Generalized Weighted
Mean and Compact Operators,” Journal of
Mathematical Analysis and Applications, Vol. 391,
no. 1, pp. 67-81, 2012.
- M. Başarır and E. E. Kara, “On the mth Difference
Sequence Space of Generalized Weighted Mean and
Compact Operators,” Acta Mathematica Scienta,
Vol. 33, no. B(3), pp. 797-813, 2013.
- M. Başarır and E. E. Kara, “On Compact Operators
on the Riesz Bm-Difference Sequence Space,”
Iranian Journal of Science & Technology, Vol.35,
no. A4, pp. 279-285, 2011.
- M. Başarır and E. E. Kara, “On some Difference
Sequence Spaces of Weighted Means and Compact
Operators,” Annals of Functional Analysis, Vol.2,
no. 2 pp. 116-131, 2011.
- E. E. Kara, “Some Topological and Geometrical
Properties of New Banach Sequence Spaces,”
Journal of Inequalities and Applications, Vol. 2013,
no. 38, 16 Pages, 2013, doi:10.1186/1029-242X2013-38.
- E. E. Kara and M. İlkhan, “ On Some Banach
Sequence Spaces Derived by a New Band Matrix,”
British Journal of Mathematics & Computer
Science, Vol.9, no. 2, pp. 141-159, 2015.