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This analysis defines new sequence spaces using a triangular q-Fibonacci matrix, suggesting practical applications in topology.
In this study, we construct a new triangular q?analogue of the q?Fibonacci matrix f?q =(fnk(q)) defined by fnk(q) = {qk fk(q)/f0n+2(q)?1, 1 ? k ? n, otherwise. After, we use the analogue to define the sequence spaces c( f?q), c0( f?q), ??( f?q), ?p( f?q) (1 ? p < ?). Then, we provide some inclusion relations for these spaces and examine a few topological characteristics. Furthermore, we construct a basis for the space ?p( f?q), calculate ??, ??, ??duals of the same space, characterize certain matrix classes, and look at some geometric properties.
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Atabey et al. (2025) studied this question.
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