Kilar, Neslihan2024-11-072024-11-0720232687-4814https://hdl.handle.net/11480/11571The present paper deals with the Fubini type numbers and polynomials with their generating functions and functional equations. By using these functions, some properties and applications of these polynomials are investigated. Many relations and computation formulas connected with the Stirling type numbers, the Apostol type polynomials and numbers of order ?r, the Bernoulli polynomials of order ?r, the Euler polynomials and numbers of order ?r, the Fubini type numbers and polynomials of order ?r and combinatorial numbers are given. Applying the derivative operator to the generating functions of these polynomials, some formulas and combinatorial sums including these numbers and polynomials are also given. Moreover, applying the Riemann integral to some formulas, we derive several interesting finite combinatorial sums associated with the Bernstein basis functions, the Cauchy numbers and the Stirling type numbers. © 2023, MTJPAM Turkey. All rights reserved.eninfo:eu-repo/semantics/closedAccessBernstein basis functionsCauchy numberscombinatorial numbersFubini type numbers and polynomialsgenerating functionspecial numbersStirling numbersArticle53 Special Issue23362-s2.0-85172663285N/A