Strongly(Vλ, A, Δn(vm),p, q)-summable sequence spaces defined by modulus function and statistical convergence

Authors

  • Mohammad Aiyub University of Bahrain.

DOI:

https://doi.org/10.4067/S0716-09172015000200007

Keywords:

De la Vallee-Poussin mean, Difference operator, Modulus function, Statistical convergence.

Abstract

In this paper we introduce strongly (Vλ,A, Δnvm,p, q)-summable sequences and give the relation between the spaces of strongly (Vλ,A, Δnvm,p, q)-summable sequences and strongly (Vλ,A, Δnvm,p, q)-summable sequences with respect to a modulus function when A =(aik) is an infinite matrix of complex number, (Δnvm) is generalized difference operator, p = (pi) is a sequence of positive real numbers and q is a seminorm. Also we give the relationship between strongly (Vλ,A, Δnvm,p, q) - convergence with respect to a modulus function and strongly Sλ(A, Δn(vm))- statistical convergence.

Author Biography

Mohammad Aiyub, University of Bahrain.

Department of Mathematics.

References

[1] M. Aiyub, Strongly almost summable difference sequences and statistical convergence., Advances in Mathematics: Scientific Journal 2 (1), pp. 1-8, (2013).

[2] T. Bilgin, Some sequence spaces defined by modulus., Int. Math. J., 3 (3), pp. 305-310, (2003).

[3] J. S. Connor, The statistical and strong p — Cesao convergence of sequence., Analysis 8 (1998), pp. 47-63, (1998).

[4] H. Dutta, Characterization of certain matrix classes involving generalized difference summability spaces., Appl. Sci. Apps 11, pp. 60-67, (2009).

[5] M. Et and R. Colak, On generalized difference sequence spaces., Soochow J. Math 21 (4), pp. 147-169, (1985).

[6] H. Fast, Sur la convergence statistique., Colloq. Math. 2, pp. 241-244, (1951).

[7] A. R. Freedman and J. J. Sember, Density and summability., Pacific. J. Math., 95, pp. 293-305, (1981).

[8] M. Güngör, M. Et and Y. Altin, Strongly (va, A , q)-summable sequences defined by Orlicz functions., Appl.Math. Comput., 157, pp. 561-571, (2004).

[9] H. Kizmaz, On certain sequence spaces, Canad. Math. Bull. 24, pp. 169-176, (1981).

[10] E. Kolk, On strong boundedness and summability with respect to a sequence moduli., Tartu Ul Toimetised 960, (1983).

[11] L. Lindler, Uber de la Valle-pousinche Summierbarkeit Allgemeiner Orthogonalreihen., Acta Math. Acad. Sci. Hungar. 16, pp. 375-387, (1995).

[12] I. J. Maddox, Sequence spaces defined by a modulus., Mat. Proc. Camb. Phil. Soc. 100, pp. 161-166, (1986).

[13] I. J. Maddox, Inclusion between FK space and Kuttner’s theorem., Math. Proc. Cambridge. Philos. Soc. 101, pp. 523-527, (1987).

[14] S. Mohiuddin and M. Aiyub, Lacunary statistical convergence in random2-normed spaces., Appl. Math. Inf. Sci. 6(3), pp. 581-585, (2012).

[15] H. Nakano, Concave modulars, J. Math. Soc. Japan, 5, pp. 29-49, (1953).

[16] E.Ozturk and T. Bilgin, Strongly summable sequence spaces defined by a modulus., Indian J. Pure and App. Math. 25, pp. 621-625, (1994).

[17] W. H. Ruckle, FK spaces in which the sequence of coordinate vector is bounded., Canad. J. Math. 25, pp. 973-978, (1973).

[18] D.Rath and B.C. Tripathy,Matrix maps on sequence spaces associated with sets of intergers., Indian journal of pure Apll. Math. 27 (2), pp. 197-206, (1996).

[19] T.Salat, On Statistically convergent sequence of real numbers., Math. Slovaca 30, pp. 139-150, (1980).

[20] E. Savas, Some sequence spaces and statistical convergence., Int.J. Math. and Math. Sci., 29 (5), pp. 303-306, (2002).

[21] I. J. Schoenberg, The integrability of certain functions and related summability methods., Amer. Math. Monthly, 66, pp. 261-375, (1959).

[22] B. C. Tripathy, Matrix transforations between some classes of sequences, Journal of Mathematical Analysis and appl. 206, pp. 448-450, (1997).

[23] B. C. Tripathy and A. Esi, A new type of difference sequence spaces., Int. J. Sci. Technol. 1 (1), pp. 11-14, (2006).

[24] B. C. Tripathy ,A. Esi and B. K. Tripathy,On a new type of generalized difference cesaro sequence spaces., Soochow J. Math 31 (3), pp. 333- 340, (2005).

[25] B. C. Tripathy and M. Sen, On generalized statitically convergent sequences, Indian journal of pure and App. Maths. 32 (11), pp. 1689- 1694, (2001).

[26] B. C. Tripathy and M. Sen, Characterization of some matrix classes involving paranormed sequence spaces, Tamkang Jour. Math, 37 (2), pp. 155-162, (2006).

How to Cite

[1]
M. Aiyub, “Strongly(Vλ, A, Δn(vm),p, q)-summable sequence spaces defined by modulus function and statistical convergence”, Proyecciones (Antofagasta, On line), vol. 34, no. 2, pp. 191-203, 1.

Issue

Section

Artículos

Similar Articles

You may also start an advanced similarity search for this article.