Almost convergent sequence spaces derived by the domain of quadruple band matrix
Keywords:
matrix domain, Schauder basis, beta- and gamma-duals, Banach Limits, almost convergence and matrix classesAbstract
In this work, we construct the sequence spaces f(Q(r,s,t,u)), f0(Q(r,s,t,u)) and fs(Q(r,s,t,u)), where Q(r,s,t,u) is quadruple band matrix which generalizes the matrices Δ3, B(r,s,t), Δ2, B(r,s) and Δ, where Δ3, B(r,s,t), Δ2, B(r,s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β-, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.
References
Ahmad, Zaheer, and Mohammad Mursaleen. "Köthe-Toeplitz duals of some new sequence spaces and their matrix maps." Publ. Inst. Math. (Beograd) (N.S.) 42(56): 57-61.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Bektas, Çigdem Asma, and Rifat Çolak. "On the Köthe-Toeplitz duals of some generalized sets of difference sequences." Demonstratio Math. 33, no. 4 (2000): 797-803.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Basar, Feyzi, and Murat Kirisçi. "Almost convergence and generalized difference matrix." Comput. Math. Appl. 61, no. 3 (2011): 602-611.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Basar, Feyzi, and Rifat Çolak. "Almost-conservative matrix transformations." Doga Mat. 13, no. 3 (1989): 91-100.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Basar, Feyzi. "Strongly-conservative sequence-to-series matrix transformations." Erc Üni Fen Bil Derg. 5, no. 12 (1989): 888-893.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Basar, Feyzi, and Ihsan Solak. "Almost-coercive matrix transformations." Rend. Mat. Appl. (7) 11, no. 2: 249-256.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Basar, Feyzi. "f-conservative matrix sequences." Tamkang J. Math. 22, no. 2 (1991): 205-212.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Basar, Feyzi. Summability Theory and Its Applications. Vol. 44 of Nijhoff International Philosophy Series. Istanbul: Bentham Science Publishers, 2012.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Basar, Feyzi and Hemen Dutta. Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties. Monographs and Research Notes in Mathematics. Boca Raton, London, New York: CRC Press, Taylor & Francis Group, 2020.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Basarir, Metin and Mustafa Kayikçi. On the generalized Bm-Riesz difference sequence space and beta-property. J. Inequal. Appl. 2009, Art. ID 385029.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Bektas, Çigdem Asma. "On some new generalized sequence spaces." J. Math. Anal. Appl. 277, no. 2 (2003): 681-688.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Boos, Johann. Classical and Modern Methods in Summability. Oxford Mathematical Monographs. New York: Oxford University Press Inc., 2000.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Choudhary, B., and Sudarsan Nanda. Functional Analysis with Applications. New York: John Wiley & sons Inc., 1989.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Duran, J. Peter. "Infinite matrices and almost-convergence." Math. Z. 128 (1972): 75-83.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Et, Mikâil, and Rifat Çolak. "On some generalized difference sequence spaces." Soochow J. Math. 21, no. 4 (1995): 377-386.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Et, Mikâil. "On some difference sequence spaces." Doga Mat. 17, no. 1 (1993): 18-24.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jarrah, Abdullah M., and Eberhard Malkowsky. "BK spaces, bases and linear operators." Rend. Circ. Mat. Palermo (2) Suppl. No.52 (1998): 177-191.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kızmaz, Hüsnü. "On certain sequence spaces." Canad. Math. Bull. 24, no. 2 (1981): 169-176.
##plugins.generic.googleScholarLinks.settings.viewInGS##
King, Jerry Porter "Almost summable sequences." Proc. Amer. Math. Soc. 17 (1966): 1219-1225.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Kirisçi, Murat, and Feyzi Basar. "Some new sequence spaces derived by the domain of generalized difference matrix." Comput. Math. Appl. 60, no. 5 (2010): 1299-1309.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Lorentz, George Gunther. "A contribution to the theory of divergent sequences." Acta Math. 80 (1948): 167-190.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Maddox, Ivor John. Elements of Functional Analysis. Cambridge, New York, New Rochelle, Melbourne, Sydney: Cambridge University Press, 1988.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Mursaleen, Mohammad. "Generalized spaces of difference sequences." J. Math. Anal. Appl. 203, no. 3 (1996): 738-745.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Mursaleen, Mohammad. Applied Summability Methods. Heidelberg, New York, Dordrecht, London: Springer Briefs, 2014.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Mursaleen, Mohammad and Basar, Feyzi. Sequence Spaces: Topics in Modern Summability Theory. Boca Raton, London, New York: CRC Press, Taylor & Francis Group, 2020.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Öztürk, Ekrem. "On strongly regular dual summability methods." Comm. Fac. Sci. Univ. Ankara Sér. A1 Math. 32, no. 1 (1983): 1-5.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Siddiqi, Jamil Ahmad. "Infinite matrices summing every almost periodic sequence." Pacific J. Math. 39 (1971): 235-251.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Sönmez, Abdulcabbar. "Some new sequence spaces derived by the domain of the triple band matrix." Comput. Math. Appl. 62, no. 2 (2011): 641-650.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Sönmez, Abdulcabbar. "Almost convergence and triple band matrix." Math. Comput. Model. 57, no. 9-10 (2013): 2393-2402.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Wilansky, Albert. Summability Through Functional Analysis. Vol. 85 of North-Holland Mathematics Studies. Amsterdam, New York, Oxford: Elsevier Science Publishers, 1984.
##plugins.generic.googleScholarLinks.settings.viewInGS##
