Difference sequence spaces in cone metric space
DOI:
https://doi.org/10.4067/S0716-09172014000400006Keywords:
Cone metric, complete metric space, difference sequence, solid space, symmetric space, métrica cónica, espacio métrico completo, secuencia diferencial, espacio sólido, espacio simétrico.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.Downloads
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References
[1] T. Abdeljawad, Completion of cone metric spaces, Hacettepe Jour. Math. Stat., 39 (1), pp. 67-74, (2010).
[2] I. Beg, M. Abbas and T. Nazir, Generalized cone metric space, J. Nonlinear Sci. Appl., 3 (1), pp. 21-31, (2010).
[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).
[4] H. Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24, pp. 169-176, (1981).
[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).
[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).
[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.
[9] B. C. Tripathy and P. Chandra, On some generalized difference paranormed sequence spaces associated with multiplier sequences defined by modulus function, Anal. Theory Appl., 27 (1), pp. 21-27, (2011).
[10] B. C. Tripathy and S. Debnath, On generalized difference sequence spaces of fuzzy numbers, Acta Scientiarum. Technology, 35 (1), pp. 117-121, (2013).
[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).
[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).
[2] I. Beg, M. Abbas and T. Nazir, Generalized cone metric space, J. Nonlinear Sci. Appl., 3 (1), pp. 21-31, (2010).
[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).
[4] H. Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24, pp. 169-176, (1981).
[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).
[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).
[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.
[9] B. C. Tripathy and P. Chandra, On some generalized difference paranormed sequence spaces associated with multiplier sequences defined by modulus function, Anal. Theory Appl., 27 (1), pp. 21-27, (2011).
[10] B. C. Tripathy and S. Debnath, On generalized difference sequence spaces of fuzzy numbers, Acta Scientiarum. Technology, 35 (1), pp. 117-121, (2013).
[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).
[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).
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Published
2017-03-23
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How to Cite
[1]
“Difference sequence spaces in cone metric space”, Proyecciones (Antofagasta, On line), vol. 33, no. 4, pp. 437–446, Mar. 2017, doi: 10.4067/S0716-09172014000400006.