A New Series Space Derived By Absolute Generalized Norlund Means

Abstract

In a way different from traditional methods, recently, new series spaces have been established by using absolute summability methods. Among these absolute summability methods, the absolute generalized Norlund summability method |N; p(n), q(n), theta(n)|(k) is extremely important as it includes several summability methods such as absolute Norlund, weighted, Cesaro and Euler summability methods. Now, it is natural to ask behavior of the space derived by the absolute summability of generalized Norlund means. The purpose of this study is to derive a more general series space including some well known spaces such as the spaces fifi |(N) over bar (theta)(q)|(k), |C-alpha|(k), |C-alpha,C-beta|(k), |N-p(theta)|(k) and |E-r(theta)|(k) to investigate its topological structure, alpha-, beta- and gamma-duals. Beside this, some matrix transformations related to these spaces have been characterized.