Kucukoglu, Irem2026-01-242026-01-242024https://hdl.handle.net/20.500.12868/4741The essential target of this study is to introduce multivariable and multiparameter generalization of the Hermite-based Peters-type Simsek numbers and polynomials and to construct their generating functions. Besides, inspired by the generating functions and techniques constructed by Simsek [25], we here introduce and systematically investigate some new families of generating-type functions whose functional equations have been used to reveal generating functions for new families of special numbers and polynomials in this paper. The constructed generating functions unify and generalize, but are not limited to, the generating functions for the Hermite-based Peters-type Simsek numbers and polynomials, the positive and negative higher-order Peters-type Simsek numbers and polynomials, the Peters-type Simsek numbers and polynomials of all kinds, the two-variable Peters-type Simsek polynomials, the two-variable Changhee polynomials. We finalize this paper by putting forward some comments involving open problems and observations on the main results. © 2024, MTJPAM Turkey. All rights reserved.eninfo:eu-repo/semantics/closedAccesscomputation formulasGenerating functionsHermite polynomialsPeters-type Simsek numbers and polynomialsspecial functionsspecial numbers and polynomialsspecial sequencesunified presentationArticle63 Special Issue2172382-s2.0-85199299877Q1