On A New Almost Convergent Sequence Space Defined By The Matrix ∆_u^λ

Year 2020, , 321 - 329, 15.04.2020

Gülsen Kılınç

https://doi.org/10.17714/gumusfenbil.639476

Abstract

In
this study, it is defined almost sequence spaces f(Λ ̂ ), f_0(Λ ̂ ) and fs(Λ ̂ ) as domain of the
matrix . ∆_u^λ Some topological
properties of these spaces are investigated and determined β-,  γ- duals of aforementioned sequence space. Futhermore, it is
characterized the class of matrices (f(Λ ̂ ): μ), (fs(Λ ̂ ):μ),( μ:f(Λ ̂ )) and  ( μ:fs(Λ ̂), where μ is any given
sequence space. 

Keywords

Almost convergent, dual spaces, matrix transformations, matrix domain of a sequence space, sequence spaces

∆_u^λ Matrisi Yardımıyla Tanımlanan Yeni Bir Hemen Hemen Yakınsak Dizi Uzayı Üzerine

Abstract

Bu
çalışmada  ∆_u^λ matrisinin etki alanları olarak f(Λ ̂ ), f_0(Λ ̂ ) ve fs(Λ ̂ ) hemen hemen
yakınsak dizi uzayları tanımlandı. Bu uzayların bazı topolojik özellikleri
incelendi ve β-,  γ- dualleri belirlendi.
Ayrıca,(f(Λ ̂ ): μ), (fs(Λ ̂ ):μ),( μ:f(Λ ̂ )) ve ( μ:fs(Λ ̂),  matris sınıfları karakterize edildi.

Keywords

Hemen hemen yakınsaklık, dual uzaylar, matris dönüşümleri, bir dizi uzayının matris etki alanı, dizi uzayları

References

• Başar, F., 1989. Strongly-conservative sequence to series matrix transformations, Erc. Üni. Fen Bil. Derg. 5, (12), 888–893.
• Başar, F. and Çolak, R., 1989. Almost-conservative matrix transformations, Turkish J. Math, 13, (3), 91- 100.
• Başar, F., 1991. f -conservative matrix sequences, Tamkang J. Math, 22, (2), 205–212..
• Başar, F. and Solak, İ., 1991. Almost-coercive matrix transformations, Rend. Mat. Appl. 7, (11) 249–256.
• Başar, F. and Kirişçi, M., 2011. Almost convergence and generalized difference matrix, Comput. Math. Appl. 61, 602-611.
• Başar, F., 2012. Summability Theory and Its Applications, Bentham Science Publishers ebooks, Monographs, xi+405 pp, ISB:978-1-60805-252-3, İstanbul
• Butkovic, D., Kraljevic, H. and Sarapa, H. N., 1987. On the almost convergence, in Functional analysis, II, Lecture Notes in Mathematics, 1242, 396417, (Springer, Berlin, Germany).
• Candan, M., 2012. Domain of the double sequential band matrix in the classical sequence spaces, Journal of Inequalities and Applications 2012 (1), 2012:281, 15 pages.
• Candan, M., 2014. Some New Sequence Spaces Derived from the Spaces of Bounded, Convergent and Null Sequences, International Journal of Modern Mathematical Sciences, 12(2), 74-87.
• Candan, M., 2014. Domain of the double sequential band matrix in the spaces of convergent and null sequences, Advances in Difference Equations 2014:163, 18 pages.
• Candan, M., 2014. Almost convergence and double sequential band matrix, Acta Math. Scientia, 34, (2), 354–366.
• Candan, M. and Kayaduman, K., 2015. Almost Convergent sequence space Reproduced By Generalized Fibonacci Matrix and Fibonacci Core, British J. Math. Comput. Sci. 7, (2), 150-167.
• Candan, M., 2018. A New Outlook for Almost Convergent Sequence Spaces, Cumhuriyet Sci. J. 39, (1), 34-46.
• Duran, J. P., 1972. Infinite matrices and almost convergence, Math. Z. 128, 75-83.
• Ganie, A. and Sheikh, N. A., 2013. On some new sequence spaces of non-absolute type and matrix transformations, Egyptian Mathematical Society, 21, 108-114.
• Jarrah, A. M., and Malkowsky, E., 1990. BK- spaces, bases and linear operators, Ren. Circ. Mat. Palermo, 2, (52), 177–191.
• Karaisa, A. and Özger, F., 2015. Almost difference sequence spaces reproduced by using a generalized weighted mean, J. Comput. Anal. and Appl. 19, (1), 27–38.
• Kayaduman, K. and Şengönül, M.,(a) 2012. On the Riesz almost convergent sequence space, Abstr. Appl. Anal. 2012, article ID: 691694, 18 pages.
• Kayaduman, K. and Şengönül, M., (b) 2012. The space of Cesaro almost convergent sequence and core theorems, Acta Mathematica Scientia, 6, 2265–2278.
• King, J. P., 1966. Almost summable sequences, Proc. Amer. Math. Soc. 17, 1219 -1225.
• Kirisçi, M., 2012. Almost convergence and generalized weighted mean, AIP Conf. Proc, 1470,191–194.
• Kirisçi, M., 2014. Almost convergence and generalized weighted mean II, J.Ineq. and Appl., 1, 93, 13pages.
• Lorentz, G. G.,1948. A contribution to the theory of divergent sequences, Acta Mathematica, 80, 167-190.
• Móricz, F. and Rhoades, B. E., 1990. Some characterizations of almost convergence for single and double sequences. Publ. Inst. Math Nouv S`er, 48, (62), 61–68.
• Öztürk, E.,1983. On strongly regular dual summability methods, Commun. Fac. Sci. Univ. Ank. Series: A_1, Math., Stat. 32, 1-5.
• Sıddıqi, J. A., 1971. Infinite matrices summing every almost periodic sequences, Pacific J. Math, 39, (1), 235–251.