Coincidence points principle for mappings in partially ordered spaces (Q465845)

Modifying the concept of covering, the authors present the theory of covering for mappings acting in partially ordered spaces \(X\) and \(Y\). Examples are given to illustrate the theory. Using this theory, they devote the rest of the paper to studying the existence of coincidence points of isotone and orderly covering mappings in spaces \(X\) and \(Y\). As a consequence, classical fixed point theorems of G. Birkhoff, A. Tarski, B. Knaster (cf. \textit{A. Granas} and \textit{J. Dugundji} [Fixed point theory. New York, NY: Springer (2003; Zbl 1025.47002)]) and other results are derived.