Recently, Kim-Kim introduced the degenerate Whitney numbers of the first and second kind involving the degenerate Dowling polynomials and numbers. In this paper, we introduce the fully degenerate Dowling polynomials and the fully degenerate Bell polynomials and derive some identities involving these polynomials. We also obtain the generating functions, expressions, and recurrence relations for the fully degenerate Dowling polynomials and the fully degenerate Bell polynomials and other special polynomials and numbers.

Dedekind-type DC sums and their properties are defined in terms of Euler functions. Ma et al. recently introduced poly-Dedekind-type DC sums and demonstrated that they satisfy a reciprocity relation. In this paper, we introduce the degenerate poly-Euler polynomials and numbers, and we also consider the reciprocity relations of degenerate poly-Dedekind-type DC sums. Equivalently, several properties and identities of degenerate poly-Euler functions are obtained.

Based on the degenerate unipoly-Euler functions and type 2 degenerate unipoly-Euler functions, we first introduce the two types of degenerate unipoly-Dedekind type DC (Daehee-Changhee) sums. By using the definitions of unipoly functions, degenerate Stirling numbers of the first kind and the second kind, degenerate Genocchi polynomials, and degenerate Genocchi numbers, we obtain several combinatorial identities and properties of the degenerate unipoly-Euler functions and the type 2 degenerate unipoly-Euler functions. The two types of degenerate unipoly-Dedekind type DC sums are shown to satisfy reciprocity relations.