A New Series Space Derived by Absolute Generalized Nörlund Means

Abstract

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 Nörlund summability method |N, p n , q n , θ n | k is extremely important as it includes several summability methods such as absolute Nörlund, weighted, Cesàro and Euler summability methods. Now, it is natural to ask behavior of the space derived by the absolute summability of generalized Nörlund means. The purpose of this study is to derive a more general series space including some well known spaces such as the spaces | N ˜ q θ | k ${\left| {\tilde N_q^\theta } \right|_k}$ , |C α | k , |C α, β | k , | N p θ | k ${\left| {N_p^\theta } \right|_k}$ and | E r θ | k ${\left| {E_r^\theta } \right|_k}$ , and to investigate its topological structure, α-, β- and γ-duals. Beside this, some matrix transformations related to these spaces have been characterized.