Bounded linear operator for some new matrix transformations

• Aiyub, Mohammad ^[1]
  1. [1] University of Bahrain

     University of Bahrain

     Baréin

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 31, Nº. 3, 2012, págs. 209-217
• Idioma: inglés
• DOI: 10.4067/S0716-09172012000300002
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we define (σ, 0)-convergence and characterize (σ, θ)-conservative, (σ, 0)-regular, (σ, 0)-coercive matrices and we also determine the associated bounded linear operators for these matrix classes.

• Referencias bibliográficas
  • Citas [1] B. Aydin,Lacunary almost summability in certain linear topological spaces, Bull. Malays Math.Sci.Soc. 2, pp. 217-223, (2004).
  • [2] S.Banach, Theorie des operations lineaires (Warsaw), (1932).
  • [3] C. C ¸ akan, B. Altay and H. C ¸ o¸ skun, σ-regular matrices and a σ-core theorem for double sequences, Hacettepe J. Math. Stat., 38 (1),...
  • [4] C. Cakan, B. Altay and M. Mursaleen, The σ-convergence and σ-core of double sequences, Applied Mathematics Letters, 19, pp. 1122-1128,...
  • [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,...
  • [14] M. Mursaleen and S.A.Mohiuddine, On σ-conservative and boundedly σ-conservative four dimensional matrices,Computers and Mathematics with...
  • [15] M. Mursaleen and S.A.Mohiuddine, Some inequalities on sublinear functionals related to the invariant mean for double sequences, Math....
  • [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).