Generalised Difference Sequence Space of non-absolute Type

A.H. Ganie; S. A. Lone; A. Afroza

doi:10.20885/EKSAKTA.vol1.iss2.art9

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August 23, 2019

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May 16, 2020

Published

June 15, 2020

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Abstract

It was Shiue [16] who have introduced the Cesaro spaces of the type Cesp and Ces1.In view of Chiue, we shall introduce and study some properties of generalised Cesaro difference sequence space. We also examine some of their basic properties viz., BK property and some inclusions relations will be taken care of.

Keywords

Difference sequence Cesaro sequence space $BK$-space

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How to Cite

Ganie, A., A. Lone, S., & Afroza, A. (2020). Generalised Difference Sequence Space of non-absolute Type. EKSAKTA: Journal of Sciences and Data Analysis, 20(2), 147–153. https://doi.org/10.20885/EKSAKTA.vol1.iss2.art9

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References

M. Basarir, Paranormed Cesaro dierence sequence space and related matrixtransformation, Turk. J. Math., 15(1991), 14-19.
V. K. Bhardwaj and N. Sing, On some new spaces of lacunary strongly-convergent sequences dened by Orlicz functions, Indian J. Pure Appl. Math.,31(11)(2000), 1515-1526.
M. Et, On some generalised Cesaro dierence sequence spaces, Istanbul Univ. FenFak. Mat. Derg., 55(56)(1996/97), 221-229.
A. R. Freedman, J. J. Sember and M. Raphael, Some Cesaro type summabilityspaces, Proc. Lond. Math. Soc., 37(1978), 508-520.
A. A. Jagers, A note on Cesaro sequence spaces, Nieuw. Arch. Wisk., 22(3)(1974),113-124.
A. H. Ganie and A. Antesar, Certain sequence spaces, Adv. Stu. in Comtem.Math., 30(1)(2020), 17-27.
A. H. Ganie and N. A. Sheikh, Matrix transformation into a new sequence spacerelated to invariant means, Chamchuri J. Math., 4(12)(2012), 71-72.
A. H. Ganie and N. A. Sheikh, On some new sequence space of non-absolute typeand matrix transformations, Jour. Egyptain Math. Soc., 21( 2013), 34-40.
A. H. Ganie and N. A. Sheikh, Innite matrices and almost bounded sequences,Vietnam J. Math, 42(2)(2014), 153-157.
A. H. Ganie, A. Mobin N. A. Sheikh and T. Jalal, New type of Riesz sequencespace of non-absolute type, J. Appl. Comput. Math., 5(1)(2016), 1-4.
A. H. Ganie, N. A. Sheikh, M. Ahmad and Afroza, Some matrix mappings of-means, Asian Journal of Mathematics and Computer Research,13(2)(2016), 119-124.
A. H. Ganie and N. A. Sheikh, Innite matrices and almost convergence, Filomat,29(6) (2015), 1183-1188.
A. H. Ganie, B. C. Tripathy, N. A. Sheikh and M. Sen, Invariant means and matrixtransformations, Func. Anal.-TMA, 2 (2016), 28-33.
T. Jalal, S. A. Gupkari and A. H. Ganie, Innite matrices and sigma convergentsequences, Southeast Asian Bull. Math., 36 (2012), 825-830.[15] V. Karakaya, H. Kara and R. Savas, On strongly Cesaro convergent sequencespaces dened by Orlicz function, Analele Universitatii din Timisoara, XL,(2)(2002), 67-74.
H. Kizmaz, On certain sequence, Canad, Math. Bull., 24(2) (1981), 169-176.
M. Mursaleen, A. H. Ganie and N. A. Sheikh, New type of generalized dierencesequence space of non-absolute type and some matrix transformations, Filomat,28(7)2014), 1381-1392.
P.-N, Ng and P.-Y.Lee, Cesaro sequences spaces of non-absolute type, Comment.Math. Prace Mat., 20(2)(1978), 429-433.
F. Nuray and E.Savas, Some new sequence spaces dened by a modulus function,Indian J. Pure Appl. Math., 24 (4)(1993), 657-663.
C. Orhan, Cesaro dierence sequence spaces related matrix transformations,Comm. Fac. Sci. Univ. Ankara Ser. A1 Math., 32(8)(1983), 55-63.
E. Savas, Spaces of strongly lacunary invariant summable sequences, Tbilisi Math.J., 13(1)(2020), 61-68.
E. Savas and R. Savas, Some sequence spaces dened by Orlicz function, Arch.Math. (Brno), 40(2004), 33-40.
E. Savas, Lacunary almost convergence and some new sequence spaces, Filomat,33(5)(2019), 1397-1402.
N. A. Sheikh and A. H. Ganie, A new paranormed sequence space and some matrixtransformation, Acta Math. Academiae Paedag. Nyiregy., 28 (2012), 47{58.
J. S. Shiue, On the Cesaro sequence space, Tamkang J. Math., 2(1970), 19-25.
B. C. Tripathy and A. Esi, A new type of dierence sequence spaces, Int. J. Sci.Tech., 1(1)(2006), 11-14.
B. C. Tripathy, A. Esi and B. K. Tripathy , On a new type of generalized dierenceCesaro sequence spaces, Soochow J. Math., 31(3)(2005), 333-340.

References

M. Basarir, Paranormed Cesaro dierence sequence space and related matrixtransformation, Turk. J. Math., 15(1991), 14-19.

V. K. Bhardwaj and N. Sing, On some new spaces of lacunary strongly-convergent sequences dened by Orlicz functions, Indian J. Pure Appl. Math.,31(11)(2000), 1515-1526.

M. Et, On some generalised Cesaro dierence sequence spaces, Istanbul Univ. FenFak. Mat. Derg., 55(56)(1996/97), 221-229.

A. R. Freedman, J. J. Sember and M. Raphael, Some Cesaro type summabilityspaces, Proc. Lond. Math. Soc., 37(1978), 508-520.

A. A. Jagers, A note on Cesaro sequence spaces, Nieuw. Arch. Wisk., 22(3)(1974),113-124.

A. H. Ganie and A. Antesar, Certain sequence spaces, Adv. Stu. in Comtem.Math., 30(1)(2020), 17-27.

A. H. Ganie and N. A. Sheikh, Matrix transformation into a new sequence spacerelated to invariant means, Chamchuri J. Math., 4(12)(2012), 71-72.

A. H. Ganie and N. A. Sheikh, On some new sequence space of non-absolute typeand matrix transformations, Jour. Egyptain Math. Soc., 21( 2013), 34-40.

A. H. Ganie and N. A. Sheikh, Innite matrices and almost bounded sequences,Vietnam J. Math, 42(2)(2014), 153-157.

A. H. Ganie, A. Mobin N. A. Sheikh and T. Jalal, New type of Riesz sequencespace of non-absolute type, J. Appl. Comput. Math., 5(1)(2016), 1-4.

A. H. Ganie, N. A. Sheikh, M. Ahmad and Afroza, Some matrix mappings of-means, Asian Journal of Mathematics and Computer Research,13(2)(2016), 119-124.

A. H. Ganie and N. A. Sheikh, Innite matrices and almost convergence, Filomat,29(6) (2015), 1183-1188.

A. H. Ganie, B. C. Tripathy, N. A. Sheikh and M. Sen, Invariant means and matrixtransformations, Func. Anal.-TMA, 2 (2016), 28-33.

T. Jalal, S. A. Gupkari and A. H. Ganie, Innite matrices and sigma convergentsequences, Southeast Asian Bull. Math., 36 (2012), 825-830.[15] V. Karakaya, H. Kara and R. Savas, On strongly Cesaro convergent sequencespaces dened by Orlicz function, Analele Universitatii din Timisoara, XL,(2)(2002), 67-74.

H. Kizmaz, On certain sequence, Canad, Math. Bull., 24(2) (1981), 169-176.

M. Mursaleen, A. H. Ganie and N. A. Sheikh, New type of generalized dierencesequence space of non-absolute type and some matrix transformations, Filomat,28(7)2014), 1381-1392.

P.-N, Ng and P.-Y.Lee, Cesaro sequences spaces of non-absolute type, Comment.Math. Prace Mat., 20(2)(1978), 429-433.

F. Nuray and E.Savas, Some new sequence spaces dened by a modulus function,Indian J. Pure Appl. Math., 24 (4)(1993), 657-663.

C. Orhan, Cesaro dierence sequence spaces related matrix transformations,Comm. Fac. Sci. Univ. Ankara Ser. A1 Math., 32(8)(1983), 55-63.

E. Savas, Spaces of strongly lacunary invariant summable sequences, Tbilisi Math.J., 13(1)(2020), 61-68.

E. Savas and R. Savas, Some sequence spaces dened by Orlicz function, Arch.Math. (Brno), 40(2004), 33-40.

E. Savas, Lacunary almost convergence and some new sequence spaces, Filomat,33(5)(2019), 1397-1402.

N. A. Sheikh and A. H. Ganie, A new paranormed sequence space and some matrixtransformation, Acta Math. Academiae Paedag. Nyiregy., 28 (2012), 47{58.

J. S. Shiue, On the Cesaro sequence space, Tamkang J. Math., 2(1970), 19-25.

B. C. Tripathy and A. Esi, A new type of dierence sequence spaces, Int. J. Sci.Tech., 1(1)(2006), 11-14.

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

Generalised Difference Sequence Space of non-absolute Type

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