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

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.