Bounded linear operator for some new matrix transformations
DOI:
https://doi.org/10.4067/S0716-09172012000300002Keywords:
Sequence spaces, invariant mean, matrix transformation, bounded linear operators, espacios secuenciales, media invariable, transformación matricial, operadores lineales acotados.Abstract
In this paper, we define (σ, θ)-convergence and characterize (σ, θ)-conservative, (σ, θ)-regular, (σ, θ)-coercive matrices and we also determine the associated bounded linear operators for these matrix classes.References
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[2] S.Banach, Theorie des operations lineaires (Warsaw), (1932).
[3] C. Çakan, B. Altay and H. Çoskun, σ-regular matrices and a σ-core theorem for double sequences, Hacettepe J. Math. Stat., 38 (1), pp. 51-58, (2009).
[4] C. Cakan, B. Altay and M. Mursaleen, The σ-convergence and σ-core of double sequences, Applied Mathematics Letters, 19, pp. 1122-1128, (2006).
[5] N. Dunford and J. T. Schwartz, Linear Operators: General theory, Pure and Appl. Math., Vol. 7, Interscience, New York, (1958).
[6] C. Eizen and G. Laush, Infinite matrices and almost convergence, Math. Japon., 14, pp. 137-143, (1969).
[7] J. P. King, Almost summable sequences, Proc. Amer. Math. Soc., 17, pp. 1219-1225, (1966).
[8] A. R. Freedman,J.J. Sember and M. Raphael, Some cesaro type summability space, Proc London Math.Soc. 37, pp. 508-520, (1978).
[9] G. G. Lorentz, A contribution to theory of divergent sequences, Acta Math., 80, pp. 167-190, (1948).
[10] M. Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford, 34 (1983), 77-86.
[11] M. Mursaleen, Some matrix transformations on equence space of invariant means, Hacettpe. J. Math and Stat, 38(3) (2009), 259-264, (2009).
[12] M. Mursaleen and S.A.Mohiuddine, Double σ-multiplicative matrices, J. Math. Anal. Appl., 327, pp. 991-996, (2007).
[13] M. Mursaleen and S.A.Mohiuddine, Regularly σ-conservative and σ-coercive four dimensional matrices, Computers and Mathematics with Applications, 56, pp. 1580—1586, (2008).
[14] M. Mursaleen and S.A.Mohiuddine, On σ-conservative and boundedly σ-conservative four dimensional matrices,Computers and Mathematics with Applications, 59, pp. 880-885, (2009).
[15] M. Mursaleen and S.A.Mohiuddine, Some inequalities on sublinear functionals related to the invariant mean for double sequences, Math. Ineq. Appl.,139(1), pp. 157-163, (2010).
[16] M. Mursaleen and S.A.Mohiuddine, Some new double sequence spaces of invariant means, Glasnik Matematicki, 45(1), pp. 139-153, (2010).
[17] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36, pp. 104-110, (1972).
Published
2012-10-28
How to Cite
[1]
M. Aiyub, “Bounded linear operator for some new matrix transformations”, Proyecciones (Antofagasta, On line), vol. 31, no. 3, pp. 209-217, Oct. 2012.
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