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

Author

Listed:
  • 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
    Faculty of Management, University Union Nikola Tesla, 11000 Belgrade, Serbia)

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.

Suggested Citation

  • Orhan Tuğ & Vladimir Rakočević & Eberhard Malkowsky, 2020. "On the Domain of the Four-Dimensional Sequential Band Matrix in Some Double Sequence Spaces," Mathematics, MDPI, vol. 8(5), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:789-:d:357652
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