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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.33 no.4 Antofagasta Dec. 2014

http://dx.doi.org/10.4067/S0716-09172014000400006 

Difference sequence spaces in cone metric space

Binod Chandra Tripathy

Institute of Advanced Study in Science and Tech.

Nanda Ram Das

Rinku Dey

Gauhati University

India


ABSTRACT

In this article we introduce the notion of difference bounded, convergent and null sequences in cone metric space. We investigate their different algebraic and topological properties.

Keywords and phrases : Cone metric, Complete metric space, Difference sequence, Solid space, Symmetric space.

AMS Classification : 40A05, 46B20, 54E35


REFERENCES

[1] T. Abdeljawad, Completion of cone metric spaces, Hacettepe Jour. Math. Stat., 39 (1), pp. 67-74, (2010).         [ Links ]

[2] I. Beg, M. Abbas and T. Nazir, Generalized cone metric space, J.Nonlinear Sci. Appl., 3 (1), pp. 21-31, (2010)).         [ Links ]

[3] G. A. Dhanorkar and J. N. Salunke, A Generalization on Fixed Point Theorem on Cone Metric Spaces with ù-Distance, Internat. Math. Forum, 6(39), pp. 1915-1919, (2011).         [ Links ]

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

[5] B. C. Tripathy, Y. Altin and M. Et, Generalized difference sequences spaces on seminormed spaces defined by Orlicz functions, Math. Slovaca, 58 (3), pp. 315-324, (2008).         [ Links ]

[6] B. C. Tripathy and A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50 (4), pp. 565-574, (2010).

[7] B. C. Tripathy and A. Baruah, M.Et, M. Gungor, On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers, Iranian Jour. Sci. Tech, Trans. A; Sci., 36 (2), pp. 147-155, (2012).         [ Links ]

[8] B. C. Tripathy and S. Borgogain, Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function, Advances in Fuzzy Systems, 2011, Article ID216414, 6 pages.         [ Links ]

[9] B. C. Tripathy and P. Chandra, On some generalized difference para-normed sequence spaces associated with multiplier sequences defined by modulus function, Anal. Theory Appl., 27 (1), pp. 21-27, (2011).         [ Links ]

[10] B. C. Tripathy and S. Debnath, On generalized difference sequence spaces of fuzzy numbers, Acta Scientiarum. Technology, 35 (1), pp. 117-121, (2013).         [ Links ]

[11] B. C. Tripathy and H. Dutta, On some new paranormed difference sequence spaces defined by Orlicz functions, Kyungpook Math J., 50 (1) , pp. 59-69, (2010).         [ Links ]

[12] B. C. Tripathy and R. Goswami, On triple difference sequences of real numbers in probabilistic normed spaces, Proyecciones Jour. Math., 33 (2) , pp. 157-174, (2014).         [ Links ]

 

Binod Chandra Tripathy

Mathematical Sciences Division

Institute of Advanced Study in cience and Technology

Paschim Boragaon; Garchuk

Guwahati - 781035,

Assam

India

e-mail : tripathybc@rediffmail.com

Nanda Ram Das

Department of Mathematics Gauhati University

Guwahati - 781014

Assam India

e-mail : rinkudey_math@rediffmail.com

Rinku Dey

Department of Mathematics Gauhati University

Guwahati - 781014,

Assam India

e-mail : nrd47@yahoo.co.in

Received : July 2014. Accepted : July 2014

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