Observations on a variant of compatibility (Q1384241)

\textit{T. L. Hicks} and \textit{L. M. Saliga} [Int. J. Math. Math. Sci. 17, No. 4, 713-716 (1994; Zbl 0816.47063)] introduced the concept of compatible maps. In the present paper the author considers the following concept of compatibility for functions: Let \(X\) be a topological space, \(C\subseteq D\subseteq X\) and let \(T,S: D\to X\). \(S\) is compatible with \(T\) on \(C\) iff whenever \(\{x_n\}\) is a sequence in \(C\) such that \(\{Sx_n\}\) is in \(D\) and \(Tx_n,Sx_n\to p\in D\), then \(TSx_n\to Sp\). If \(C=D\), we say \(S\) is compatible with \(T\). Using this concept the author obtains generalizations of results by Hicks and Saliga and others.