ACTA issues

## Some new paranormed sequence spaces defined by Euler and difference operators

Vatan Karakaya, Harun Polat

Acta Sci. Math. (Szeged) 76:1-2(2010), 87-100
57/2010

 Abstract. The spaces $\Delta c_{0}(p),$ $\Delta c(p)$ and $\Delta\ell _{\infty }(p)$ were defined by Ahmad and Mursaleen [1]. In [2], Altay and Polat also defined the sequence spaces $e_{0}^r(\Delta )$, $e_{c}^r(\Delta )$ and $e_{\infty }^r(\Delta )$, and determined the absolute Köthe--Toeplitz duals of these spaces. The main purpose of this work is to introduce some new paranormed sequence spaces defined by Euler and difference operators and to compute their $\alpha$-, $\beta$-, $\gamma$-duals. Also some of the matrix transformations has been characterized. AMS Subject Classification (1991): 46A45, 46B45 Keyword(s): paranormed sequence space, matrix mapping, Köthe--Toeplitz duals, Euler and difference sequence spaces Received October 18, 2008, and in revised form June 9, 2009. (Registered under 57/2010.)