Four Dimensional Matrix Operators on the Double Series Spaces of Weighted Means

Year 2025, Volume: 21 Issue: 2, 159 - 168, 27.06.2025

Feride Çalışır , Canan Hazar Gulec

https://doi.org/10.18466/cbayarfbe.1479195

Abstract

The main purpose in this study is to investigate some topological and algebraic properties of the double series space |N ̅_(p,q) |_k defined by the absolute double weighted summability methods for k≥1. Beside this, we determine the α-dual of the double series space |N ̅_(p,q) |_1 and the β(bp)- and γ- duals of the double series space |N ̅_(p,q) |_k for k≥1. Finally, we characterize some new four dimensional matrix transformation classes (|N ̅_(p,q) |_k,υ), (|N ̅_(p,q) |_1,υ) and (|N ̅_(p,q) |_1,L_k ), where υ denotes any spaces of double sequences "M" _u and C_p. Hence, we extend some results about weighted means to double sequences.

Keywords

Double sequences , Dual spaces , Four dimensional weighted means , Four dimensional matrix transformations , Pringsheim convergence

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