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Journal of Applied Mathematics and Computation

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Article Open Access http://dx.doi.org/10.26855/jamc.2021.12.005

New Type of Paranormed Behaviour of Spaces

Abdul Hamid Ganie1,2,*, Mashael M. AlBaidani3

1Department of Computer Science and Engineering, Birla Institute of Technology, Mesra-835215, Jharkhand, India.

2Department of Mathematics, Birla Institute of Technology, Mesra-835215, Jharkhand, India.

3IT Services, MECON Limited, Ranchi-834002, Jharkhand, India.

*Corresponding author: Abdul Hamid Ganie

Published: November 3,2021

Abstract

Sequence spaces play a good role in summability fields in analysis. It was Kizmaz in H. Kizmaz, who introduced the concept of difference sequences spaces on ʆ, c and c0 where ʆ c  and c0 represents space of all bounded sequences, space of convergent sequence and the sequences converging to zero. In certain cases, the most general linear operator between two sequence spaces is given by an infinite matrix. So the theory of matrix transformations has always been of great interest in the study of sequence spaces. The sequences which were studied by Kizmaz were later studied by many authors and introduced different spaces. The authors in A. H. Ganie, et al. have recently studied the spaces bvc (g,p) and bv0 (g,p) and interesting properties were analyzed. In this regard, the aim of this paper is to introduce the space bv (g,p). It will be shown to be complete linear paranormed and prove that it is linearly isomorphic to the space ʆ (p).

References

[1] I. J. Maddox. (1967). Spaces of strongly summable sequences. Quart. J. Math. Oxford, 18(2), 345-355. 

[2] B. Altay and F. Basar. (2003). On the space of sequences of p-bounded variation and related matrix mappings. Ukarnian Math. J., 1(1), 136-147.

[3] D. Fathima and A. H. Ganie. (2021). On some new scenario of Delta-spaces. Journal of Nonlinear Sciences and Applications, 14 (2021), 163-167.

[4] A. H. Ganie and N. A. Sheikh. (2013). On some new sequence space of non-absolute type and matrix transformations. J. Egypt. Math. Soc., (2013), 34-40.

[5] K. G. Gross Erdmann. (1993). Matrix transformations between the sequence spaces of Maddox. J. Math. Anal. Appl., 180(1993), 223-238.

[6] I. J. Maddox. (1968). Paranormed sequence spaces generated by infinite matrices. Proc. Camb. Phil. Soc., 64(1968), 335-340.

[7] M. Mursaleen, A. H. Ganie, and N. A. Sheikh. (2014). New type of difference sequenence spaces and matrix transformation. Filomat, 28(7), 1381-1392.

[8] N. A. Sheikh and A. H. Ganie. (2012). A new paranormed sequence space and some matrix transformations. Acta Math. Acad. Paeda. Nyregy., 28(2012), 47-58.

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

[10] A. H. Ganie. (2021). Some new approach of spaces of non-integral order. J. Nonlinear Sci, Appl., 14(2), 89-96.

[11] A. H. Ganie and D. Fathima. (2020). Almost convergence property of generalized Riesz spaces. Journal of Applied Mathematics and Computation, 4(4), 249-253.

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

[13] A. H. Ganie, N. A. Sheikh, and T. Jalal. (2015). Matrix transformations of some sequence spaces over non-archmedian fields. J. Appl. Computat. Math., (4), 1-3.

[14] A. H. Ganie, N. A. Sheikh, and T. Jalal. (2015). On some new spaces of invariant means with respect to modulus function, The inter. Jou. Modern Math. Sciences, USA, 13(3), 210-216.

[15] A. H. Ganie, N. A. Sheikh, and T. Jalal. (2014). New type of sequence spaces and matrix transformations. The inter. Jou. Modern Math. Sciences, USA, 10(3), 125-129.

[16] A. H. Ganie, Mobin Ahmad, N. A. Sheikh, T. Jalal, and S. A. Gupkari. (2016). Some new type of difference se-quence space of non-absolute type, Int. J. Modern Math. Sci., 14(1), 116-122.

[17] A. H. Ganie. New spaces over modulus function. Boletim da Sociedade Paranaense de Matemática (in press), 1-6.

[18] P. A. Naik and T. A. Tarry. Matrix Representation of an All-inclusive Fibonacci Sequence. Asian J. Math. Stat., 11(1), 18-26.

[19] N. A. Sheikh and A. H. Ganie. (2013). New paranormed sequence space and some matrix transformations. Int. J. Mod. Math. Sci., 8(2), 185-194.

How to cite this paper

New Type of Paranormed Behaviour of Spaces

How to cite this paper: Abdul Hamid Ganie, Mashael M. AlBaidani. (2021) New Type of Paranormed Behaviour of Spaces. Journal of Applied Mathematics and Computation5(4), 273-276.

DOI: http://dx.doi.org/10.26855/jamc.2021.12.005