A parametric kind of Fubini-Fibonacci polynomials and their generalizations

Resumo

In this paper, we introduce bivariate kind of three-variable Fubini-Fibonacci polynomials and their associated numbers within the approach of Golden $F$- Calculus. Utilizing generating functions, we derive several fundamental properties, including summation theorems, recurrence relations, symmetry properties, and $F$-derivative identities. We further establish connections with, Bernoulli-Fibonacci, Euler-Fibonacci, Genocchi-Fibonacci Stirling-Fibonacci numbers of the second kind and present mu,ltiple summation formulas and convolution-type identities. The proposed approach enriches the theory of Fibonacci-based special polynomials and opens new avenues for applications in combinatorics, number theory, approximation theory, and matrix analysis.