In a groupoid \(\mathcal {G}\) , the binary operation is partial; consequently, for \(x\in \mathcal {G}\) , the left and right translations \(\mathcal {R}_x: t\mapsto tx\) and \(\mathcal {L}_x: t\mapsto x^{-1}t\) are only defined on subsets of \(\mathcal {G}\) . This partiality precludes a direct generalization of translation operators for functions on \(\mathcal {G}\) , unlike the case of globally defined translations in groups. In this work, we address this limitation for topological groupoids by using two groups \(S_{\mathcal {G}}(d)\) and \(S'_{\mathcal {G}}(r)\) , which act globally on \(\mathcal {G}\) to generalize left and right translations. These generalized translations allow us to define two novel classes of functions: strongly right and left uniformly continuous and strongly almost periodic functions on \(\mathcal {G}\) . When \(\mathcal {G}\) is a topological group, these constructions recover classical translation operators and establish relationships with well-known function spaces, providing foundational tools for harmonic analysis on non-globally symmetric structures.
