New triangular q-Fibonacci matrix

Abstract

In this study, we construct a new triangular q-analogue of the q-Fibonacci matrix fq=(f(nk)(q)) defined by f(nk)(q)=( q(k)f(k)(q)/ f(n+2)(q)-1, 1 <= k <= n 0, otherwise After, we use the analogue to define the sequence spaces c(f(q)), c0(f(q)), [infinity(f(q)), [p(f(q)) (1 <= p < infinity). 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 alpha-, beta-, gamma-duals of the same space, characterize certain matrix classes, and look at some geometric properties.