New Paranormed Sequence Spaces l_{∞}(p,λ) , c(p,λ) and c_{0}(p,λ) Generated by an Infinite Matrix

Shailendra K. Mishra , Vinod Parajuli , Sergei Silvestrov. "New Paranormed Sequence Spaces l_{∞}(p,λ) , c(p,λ) and c_{0}(p,λ) Generated by an Infinite Matrix", *International Journal of Mathematical Trends and Technology (IJMTT). *V6:176-182 February 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

**Abstract**

In this paper we introduce a set of new paranormed sequence spaces , and which are generated by an infinite lower uni triangular matrix where is an infinite matrix given by, as defined in [6] . We also compute the basis for the spaces and , obtain β – dual for all these spaces and characterize the matrix classes , and . **References**

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[6] B. Choudhary and S.K. Mishra, “On Kothe-Toeplitz duals of certain sequence spaces and their matrix transformations”, Indian J. Pure Appl. Math 24(5), pp. 291-301 , 1993

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[8] I.J. Maddox, Elements of Functional Analysis, 2nd ed, Cambridge University Press, 1970

**Keywords**

Paranormed sequence spaces, β – dual, matrix transformation