Difference sequence spaces derived by using a generalized weighted mean

Abstract

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 alpha-, beta- and gamma-duals, and obtain bases for these sequence spaces. Finally, the necessary and sufficient conditions on an infinite matrix belonging to the classes (c (u, v, Delta) : l(infinity)) and (c (u, v, Delta) : c) are obtained. (C) 2010 Elsevier Ltd. All rights reserved.