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Difference sequence spaces derived by using a generalized weighted mean
(2011) Polat H.; Karakaya, Vatan; Şimşek, Necip
In this work, we define new sequence spaces by combining a generalized weighted mean and a difference operator. Afterward, we investigate topological structures, which have completeness, AK-property, and AD-property. Also, we compute the ?-, ?- and ?-duals, and obtain bases for these sequence spaces. Finally, the necessary and sufficient conditions on an infinite matrix belonging to the classes (c(u,?,?):??) and (c(u, ?,?):c) are obtained. © 2011 Elsevier Ltd. All rights reserved.
Some paranormed Euler sequence spaces of difference sequences of order m
(2013) Karakaya, Vatan; Savaş, Ekrem; Polat H.
The main purpose of this work is to extend the sequence spaces which are defined in [KARAKAYA, V.-POLAT, H.: Some new paranormed sequence spaces defined by Euler and difference operators, Acta Sci. Math. (Szeged) 76 (2010), 87-100] and [POLAT, H.-BASAR, F.: Some Euler spaces of difference sequences of order m, Acta Math. Sci. Ser. B Engl. Ed. 27 (2007), 254-266] by using difference operator of order m, and to give their alpha, beta and gamma duals. Furthermore, we characterize some classes of the related matrix transformations. © 2013 Versita Warsaw and Springer-Verlag Wien.