homotopic relative to a map

Let \((X,\mathcal{T}_X)\) and \((Y,\mathcal{T}_Y)\) be topological spaces \(A \subseteq X\) and \(f,g: X \rightarrow Y\) resp. \(\varphi: A \rightarrow Y\) continuous maps

Then \(f\) is said to be homotopic to \(g\) relative to \(\varphi\), if there exists a homotopy relative to \(\varphi\) from \(f\) to \(g\)