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

Orhan Tuğ, Vladimir Rakočević and Eberhard Malkowsky
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Orhan Tuğ: Department of Mathematics Education, Tishk International University, 44001 Erbil, Kurdistan Region, Iraq
Vladimir Rakočević: Department of Mathematics, Faculty of Sciences and Mathematics University of Niš, Višegradska 33, 18000 Niš, Serbia
Eberhard Malkowsky: Department of Mathematics, State University Novi Pazar, Vuka Karadzica bb, 36300 Novi Pazar, Serbia

Mathematics, 2020, vol. 8, issue 5, 1-18

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.

Keywords: matrix domain; sequentially defined 4D band matrix; double sequence spaces; dual spaces; matrix transformations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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