TY  - JOUR
T1  - On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences
AU  - Erdem, Sezer
AU  - Demiriz, Serkan
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.32323/ujma.1734157
JF  - Universal Journal of Mathematics and Applications
JO  - Univ. J. Math. Appl.
PB  - Emrah Evren KARA
WT  - DergiPark
SN  - 2619-9653
SP  - 141
EP  - 148
VL  - 8
IS  - 3
LA  - en
AB  - The primary objective of this study is to construct a novel double sequence space by utilizing the domain of a 4-dimensional (4D) matrix in the space $\mathcal{L}_u$  of the absolutely summable double sequences defined via the well-known Catalan numbers. Within this framework, various algebraic and topological properties of the newly introduced space are investigated. The study further aims to compute the $\alpha$-, $\beta(bp)$-, and $\gamma$-duals of the space. Another essential part of the research involves characterizing certain classes of matrix transformations from the newly defined space to some classical double sequence spaces and vice versa. These contributions are expected to enrich the theory of sequence spaces and matrix transformations by introducing new insights based on special integer sequences.
KW  - Catalan numbers
KW  - Double sequence space
KW  - Matrix transformations
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UR  - https://doi.org/10.32323/ujma.1734157
L1  - https://dergipark.org.tr/en/download/article-file/5020136
ER  -