Strongly(Vλ, A, Δn(vm),p, q)-summable sequence spaces defined by modulus function and statistical convergence
DOI:
https://doi.org/10.4067/S0716-09172015000200007Keywords:
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.Downloads
Download data is not yet available.
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).
[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).
Downloads
Issue
Section
Artículos
License
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
How to Cite
[1]
“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, Jun. 2015, doi: 10.4067/S0716-09172015000200007.