On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

References

[1] Altay, B.—Başar, F.: The fine spectrum and the matrix domain of the difference operator Δ on the sequence space ℓ_p, (0 < p < 1), Commun. Math. Anal. 2(2) (2007), 1–11.Suche in Google Scholar

[2] Aydin, C.—Başar, F.: On the new sequence spaces which include the spaces c₀ and c, Hokkaido Math. J. 33(2) (2004), 383–398.10.14492/hokmj/1285766172Suche in Google Scholar

[3] Aydin, C.—Başar, F.: Some new sequence spaces which include the spaces ℓ_p and ℓ_∞, Demonstratio Math. 38(3) (2005), 641–656.10.1515/dema-2005-0313Suche in Google Scholar

[4] Banach, S.: Theorie des Operations Lineaires, Warzawa, 1932.Suche in Google Scholar

[5] Başar, F.: Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monograph, İstanbul, 2012.Suche in Google Scholar

[6] Başar, F.—Altay, B.: On the space of sequences of p-bounded variation and related matrix mappings, (English, Ukrainian summary) Ukrain. Mat. Zh. 55(1) (2003), 108–118; reprinted in Ukrainian Math. J. 55(1) (2003), 136–147.Suche in Google Scholar

[7] Başar, F.—Braha, N. L.: Euler-Cesàro difference spaces of bounded, convergent and null sequences, Tamkang J. Math. 47(4) (2016), 405-420.10.5556/j.tkjm.47.2016.2065Suche in Google Scholar

[8] Başar, F.—Dutta, H.: Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties, CRC Press, Taylor & Francis Group, Monographs and Research Notes in Mathematics, Boca Raton . London . New York, 2020.10.1201/9781351166928Suche in Google Scholar

[9] Başar, F.—Ki͘ri͘şçi͘, M.: Almost convergence and generalized difference matrix, Comput. Math. Appl. 61(3) (2011), 602–611.10.1016/j.camwa.2010.12.006Suche in Google Scholar

[10] Başarir, M.—Kara, E. E.: On the B-difference sequence space derived by generalized weighted mean and compact operators, J. Math. Anal. Appl. 391 (2012), 67–81.10.1016/j.jmaa.2012.02.031Suche in Google Scholar

[11] Bektaş, Ç. A.—Et, M.—Çolak, R.: Generalized difference sequence spaces and their dual spaces, J. Math. Anal. Appl. 292(2) (2004), 423–432.10.1016/j.jmaa.2003.12.006Suche in Google Scholar

[12] Beckermann, B.: The condition number of real Vandermonde, Krylov and positive definite Hankel matrices, Numer. Math. 85(4) (2000), 553–577.10.1007/PL00005392Suche in Google Scholar

[13] Bennett, G.: Lower bounds for matrices, Linear Algebra Appl. 82 (1986), 81–98.10.1016/0024-3795(86)90143-6Suche in Google Scholar

[14] Bennett, G.: Some elementary inequalities, Quart. J. Math. (2) 38 (1987), 401–425.10.1093/qmath/38.4.401Suche in Google Scholar

[15] Bennett, G.: Lower bounds for matrices II, Canad. J. Math. 44 (1992), 54–74.10.4153/CJM-1992-003-9Suche in Google Scholar

[16] Bennett, G.: Factorizing the classical inequalities, Mem. Amer. Math. Soc. 120(576) (1996).10.1090/memo/0576Suche in Google Scholar

[17] Boos, J.: Classical and Modern Methods in Summability, Oxford University Press Inc., New York, 2000.10.1093/oso/9780198501657.001.0001Suche in Google Scholar

[18] Braha, N. L.—Başar, F.: On the domain of the triangle A(λ) on the spaces of null, convergent and bounded sequences, Abstr. Appl. Anal. 2013 (2013), Art. ID 476363.10.1155/2013/476363Suche in Google Scholar

[19] Cartlidge, J. M.: Weighted Mean Matrices as Operators on ℓ_p, Ph.D. thesis, Indiana University, 1978.Suche in Google Scholar

[20] Çolak, R.—Çakar, Ö.: Banach limits and related matrix transformations, Stud. Sci. Math. Hung. 24 (1989), 429–436.Suche in Google Scholar

[21] Das, G.: Banach and other limits, J. London Math. Soc. 7 (1973), 501–507.10.1112/jlms/s2-7.3.501Suche in Google Scholar

[22] Et, M.—Çolak, R.: On some generalized difference sequence spaces, Soochow J. Math. 21 (1995), 377–386.Suche in Google Scholar

[23] Foroutannia, D.—Roopaei, H.: Bounds for the norm of lower triangular matrices on the Cesàro weighted sequence space, J. Inequal. Appl. 2017(67) (2017), 11 pp.10.1186/s13660-017-1339-6Suche in Google Scholar PubMed PubMed Central

[24] Gao, P.: On a result of Cartlidge, J. Math. Anal. Appl. 332 (2007), 1477–1481.10.1016/j.jmaa.2006.11.022Suche in Google Scholar

[25] Gao, P.: On weighted mean matrices whose l^p norms are determined on decreasing sequences, Math. Inequal. Appl. 14 (2011), 373–387.10.7153/mia-14-30Suche in Google Scholar

[26] Grosse-Erdmann, K.-G.: Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl. 180(1) (1993), 223–238.10.1006/jmaa.1993.1398Suche in Google Scholar

[27] Hardy, G. H.: An inequality for Hausdorff means, J. London Math. Soc. 18 (1943), 46–50.10.1112/jlms/s1-18.1.46Suche in Google Scholar

[28] Hardy, G. H.: Divergent Series, Oxford University press, 1973.Suche in Google Scholar

[29] Hardy, G. H.—Littlewood, J. E.—Polya, G.: Inequalities, 2nd edition, Cambridge University press, Cambridge, 2001.Suche in Google Scholar

[30] Hilbert, D.: Ein Beitrag zur Theorie des Legendre'schen Polynoms, Acta Math. 18 (1894), 155–159.10.1007/BF02418278Suche in Google Scholar

[31] İlkhan, M.—Kara, E. E.: A new Banach space defined by Euler matrix operator, Oper. Matrices 13(2) (2019), 527–544.10.7153/oam-2019-13-40Suche in Google Scholar

[32] Jarrah, A. M.—Malkowsky, E.: Ordinary, absolute and strong summability and matrix transformations, Filomat 17 (2003), 59–78.10.2298/FIL0317059JSuche in Google Scholar

[33] Kara, E. E.—Başarir, M.: On compact operators and some Euler B^(m) difference sequence spaces, J. Math. Anal. Appl. 379(2) (2011), 499–511.10.1016/j.jmaa.2011.01.028Suche in Google Scholar

[34] Kara, E. E.—İlkhan, M.: Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra 64(11) (2016), 2208–2223.10.1080/03081087.2016.1145626Suche in Google Scholar

[35] Ki͘ri͘şçi͘, M.—Başar, F.: Some new sequence spaces derived by the domain of generalized difference matrix, Comput. Math. Appl. 60(5) (2010), 1299–1309.10.1016/j.camwa.2010.06.010Suche in Google Scholar

[36] Lascarides, C. G.—Maddox, I. J.: Matrix transformations between some classes of sequences, Proc. Camb. Phil. Soc. 68 (1970), 99–104.10.1017/S0305004100001109Suche in Google Scholar

[37] Lorentz, G. G.: A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190.10.1007/BF02393648Suche in Google Scholar

[38] Mursaleen, M.: Applied Summability Methods, Springer Briefs, 2014.10.1007/978-3-319-04609-9Suche in Google Scholar

[39] Mursaleen, M.—Başar, F.: Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Taylor & Francis Group, Series: Mathematics and Its Applications, Boca Raton . London . New York, 2020.10.1201/9781003015116Suche in Google Scholar

[40] Mursaleen, M.—Başar, F.—Altay, B.: On the Euler sequence spaces which include the spaces ℓ_p and ℓ_∞ II, Nonlinear Anal. 65(3) (2006), 707–717.10.1016/j.na.2005.09.038Suche in Google Scholar

[41] Mursaleen, M.—Noman, A. K.: On the spaces of λ-convergent and bounded sequences, Thai J. Math. 8(2) (2010), 311–329.Suche in Google Scholar

[42] Mursaleen, M.—Noman, A. K.: On some new sequence spaces of non-absolute type related to the spaces ℓ_p and ℓ_∞ I, Filomat 25 (2011), 33–51.10.2298/FIL1102033MSuche in Google Scholar

[43] Mursaleen, M.—Noman, A. K.: On some new sequence spaces of non-absolute type related to the spaces ℓ_p and ℓ_∞ II, Math. Commun. 16 (2011), 383–398.Suche in Google Scholar

[44] Nanda, S.: Matrix transformations and almost boundedness, Glas. Mat. 14(34) (1979), 99–107.Suche in Google Scholar

[45] Ng, P. N.—Lee, P. Y.: Cesàro sequence spaces of non-absolute type, Comment. Math. Prace Mat. 20 (2) (1978), 429–433.Suche in Google Scholar

[46] Pecaric, J.—Peri, I.—Roki, R.: On bounds for weighted norms for matrices and integral operators, Linear Algebra Appl. 326(1–3) (2001), 121–135.10.1016/S0024-3795(00)00310-4Suche in Google Scholar

[47] Polat, H.—Başar, F.: Some Euler spaces of difference sequences of order m, Acta Math. Sci. Ser. B Engl. Ed. 27 B(2) (2007), 254–266.10.1016/S0252-9602(07)60024-1Suche in Google Scholar

[48] Roopaei, H.: Norms of summability and Hausdorff mean matrices on difference sequence spaces, Math. Inequal Appl. 22(3) (2019), 983–987.10.7153/mia-2019-22-66Suche in Google Scholar

[49] Roopaei, H.: A study on Copson operator and its associated matrix domains, J. Inequal. Appl. 2020(120) (2020), 18 pp.10.1186/s13660-020-02388-8Suche in Google Scholar

[50] Roopaei, H.: Norm of Hilbert operator on sequence spaces, J. Inequal. Appl. 2020(117) (2020), 13 pp.10.1186/s13660-020-02380-2Suche in Google Scholar

[51] Roopaei, H.—Başar, F.: On the gamma spaces including the spaces of absolutely p-summable, null and convergent sequences, Numer. Funct. Anal. Optim., under review.10.1080/01630563.2022.2056200Suche in Google Scholar

[52] Roopaei, H.—Foroutannia, D.: The norm of matrix operators on Cesàro weighted sequence space, Linear Multilinear Algebra 67(1) (2019), 175–185.10.1080/03081087.2017.1415293Suche in Google Scholar

[53] Roopaei, H.—Foroutannia, D.: The norms of certain matrix operators from ℓ_p spaces into ℓ_p(Δⁿ) spaces, Linear Multilinear Algebra 67(4) (2019), 767–776.10.1080/03081087.2018.1432547Suche in Google Scholar

[54] Roopaei, H.—Foroutannia, D.—İlkhan, M.—Kara, E. E.: Cesàro spaces and norm of operators on these matrix domains, Mediterr. J. Math. 17(4) (2020), Art. No. 121.10.1007/s00009-020-01557-9Suche in Google Scholar

[55] Sönmez, A.—Başar, F.: Generalized difference spaces of non-absolute type of convergent and null sequences, Abstr. Appl. Anal. 2012 (2012), Art. ID 435076.10.1155/2012/435076Suche in Google Scholar

[56] Stieglitz, M.—Tietz, H.: Matrix transformationen von folgenraumen eineergebnisübersicht, Math. Z. 154 (1977), 1–16.10.1007/BF01215107Suche in Google Scholar

[57] Şengönül, M.—Başar, F.: Cesàro sequence spaces of non-absolute type which include the spaces c₀ and c, Soochow J. Math. 31(1) (2005), 107–119.Suche in Google Scholar

[58] Yeşilkayagil, M.—Başar, F.: Spaces of A_λ-almost null and A_λ-almost convergent sequences, J. Egypt. Math. Soc. 23(2) (2015), 119–126.10.1016/j.joems.2014.01.013Suche in Google Scholar