ON THE SPACES OF λm-BOUNDED AND λm-ABSOLUTELY p-SUMMABLE SEQUENCES

Sinan Ercan, Çiğdem Asma Bektaş

DOI Number
10.22190/FUMI1703303E
First page
303
Last page
318

Abstract


In this paper, we give the notion of λm-boundedness and p-absolute convergence
of type λm and using these notions we define new sequence spaces. We examine
some topological and geometric properties of these spaces. We also establish some
inclusion relations concerning these spaces and characterize some matrix classes.


Keywords

BK-Spaces, triangle matrix, α-, β-, γ-duals, Schauder basis, Matrix transformations, geometric properties

Keywords


BKSpaces, triangle matrix, alpha-, beta-, gamma-duals, Schauder basis, Matrix transformations, geometric properties.

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References


A. J. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc.,40 (1936), 396-414.

A. H. Ganie, N. A. Sheikh, On some new sequence spaces of non-absolute type and matrix

transformations, J. Egyptian Math. Soc., 21, (2013) ,108-114.

A. Wilansky, Summability Through Functional Analysis, in: North-Holland Mathematics Studies,

Elsevier Science Publishers, Amsterdam, New York, Oxford, 1984.

A. M. Jarrah, E. Malkowsky, BK-spaces, bases and linear operators, Rendiconti Circ. Mat.

Palermo II, 52, 1990, 177-191.

B. Choudhary, S. Nanda, Functional Analysis with Applications, John Wiley & Sons Inc., New

Delhi, 1989.

B. Altay, F. Ba¸sar, The matrix domain and the …ne spectrum of the di¤erence operator ¢ on the

sequence space , (0    1), Commun. Math. Anal. 2(2), 1-11, 2007.

B. Altay, On the space of p-summable di¤erence sequences of order , (1 ·   1), Studia

Scientiarum Mathematicarum Hungarica 43.4 (2006), 387-402.

B. Altay, F. Ba¸sar, Generalization of the sequence space () derived by weighted mean, J. Math.

Anal. Appl., 330, 174-185, 2007.

C. Ayd¬n, F. Ba¸sar, Some new di¤erence sequence spaces, Appl. Math. Comput. 157(3), (2004),

-693.

C. R. James, Super re‡exive spaces with bases, Pasi…c J. Math., 41:2 (1972), 409-419.

E. Malkowsky and S. D. Parashar, Matrix transformations in space of bounded and convergent

di¤erence sequence of order , Analysis 17(1997), 87–97.

F. Ba¸sar, B. Altay, On the space of sequences of -bounded variation and related matrix mappings,

Ukr. Math. J., 55, 136-147, 2003.

F. Ba¸sar, Summability Theory and Its Applications, Bentham Science Publishers, 2011, ISBN:

-1-60805-252-3.

H., K¬zmaz, On certain sequence spaces, Can. Math. Bull. 24(2), 169-176, 1981.

H. Polat, B. Altay, On some new Euler di¤erence sequence spaces. Southeast Asian Bull Math,

, 30:209–220.

H. Polat, F. Ba¸sar, Some euler spaces of di¤erence sequences of order , Acta Mathematica

Scientia, 2007, 27(B)(2), 254-266.

K. Raj, A. K¬l¬çman, On certain generalized paranormed spaces, Journal of Inequalities and

Applications (2015) 2015:37, DOI 10.1186/s13660-015-0565-z.

M. Ba¸sar¬r, E. E. Kara, On the th order di¤erence sequence space of generalized weighted mean

and compact operators, Acta Math. Sci. Ser. B Engl. Ed. 33, 3 (2013), 797–813.

M. Candan, Domain of the double sequential band matrix in the spaces of convergent and null

sequences, Advances in Di¤erence Equations, 2014, 2014:163.

M. Candan, Domain of the double sequential band matrix in the classical sequence spaces, J.

Inequal. Appl. 2012, 281, 2012.

M. C. Bi¸sgin, A. Sönmez, Two new sequence spaces generated by the composition of th order

generalized di¤erence matrix, J. Inequal. Appl., doi:10.1186/1029-242X-2014-274.

M. Mursaleen and A. K. Noman, On some new sequence spaces of non-absolute type related to

the spaces  and 1 I, Filomat, vol. 25, no. 2, pp. 33-51, 2011.

M. Mursaleen, A. K. Noman, On the spaces of ¡convergent sequences and bounded sequences,

Thai J. Math, Volume 8, Number 2, 311-329, 2010.

I. J. Maddox, Elements of Functional Analysis, 2nd ed., The University Press, Cambridge, 1988.

N. L. Braha, F. Ba¸sar, On the domain of the triangle () on the spaces of null, convergent and

bounded sequences, Abstract and Apllied Analysis, Volume 2013, Article ID 476363.

N. L. Braha, On some properties of new paranormed sequence space de…ned by 2-convergent

sequences, Journal of Inequalities and Applications, 2014, 2014:273.


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