<p>The purpose of this paper is to modify generating functions for the Frobenius–Euler type Simsek numbers and polynomials. We also give some alternating generating functions for these numbers and polynomials. By using these modification generating functions, we derive many novel functional equations involving not only the Frobenius–Euler type Simsek numbers and polynomials, but also other certain classes of special numbers and polynomials. By applying binomial series with multinomial binomial coefficients to these equations, we also derive many novel and useful formulae. By the aid of moment generating functions for the geometric distribution, we give novel relations and formulae among the Frobenius–Euler type Simsek numbers and polynomials, the Apostol–Bernoulli numbers, the Stirling numbers, the moments of the geometric distribution, and other special numbers and polynomials. We also give inequalities involving the Bernoulli numbers and polynomials, the Ostrowski inequality, and the generalized Euler type identity.</p>