On the Domain of the Four-Dimensional Sequential Band Matrix in Some Double Sequence Spaces

Author:

Tuğ OrhanORCID,Rakočević VladimirORCID,Malkowsky Eberhard

Abstract

Let E represent any of the spaces M u , C ϑ ( ϑ = { b , b p , r } ) , and L q ( 0 < q < ∞ ) of bounded, ϑ -convergent, and q-absolutely summable double sequences, respectively, and E ˜ be the domain of the four-dimensional (4D) infinite sequential band matrix B ( r ˜ , s ˜ , t ˜ , u ˜ ) in the double sequence space E, where r ˜ = ( r m ) m = 0 ∞ , s ˜ = ( s m ) m = 0 ∞ , t ˜ = ( t n ) n = 0 ∞ , and u ˜ = ( u n ) n = 0 ∞ are given sequences of real numbers in the set c ∖ c 0 . In this paper, we investigate the double sequence spaces E ˜ . First, we determine some topological properties and prove several inclusion relations under some strict conditions. Then, we examine α -, β ( ϑ ) -, and γ -duals of E ˜ . Finally, we characterize some new classes of 4D matrix mappings related to our new double sequence spaces and conclude the paper with some significant consequences.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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