Coincidence theorems and generalized equilibrium in topological spaces
Let \(T:X\to Y\) and \(S:Y\to X\) be multivalued functions, then a coincidence of \(T\) and \(S\) is a point \((x_0,y_0)\in X\times Y\) such that \(x_0\in S(y_0)\) and \(y_0\in T(x_0)\). The main results of the paper present conditions under which such a coincidence must exist, generalizing results of the author and others. There are no examples in the paper, so it contains no evidence of the existence of functions that satisfy the hypotheses of the present results but not those of the ones published earlier. The paper also contains generalizations of results of \textit{S. Park} [J. Optimization Theory Appl. 95, No. 2, 409-417 (1997; Zbl 0892.90173)], from the setting of linear spaces to that of contractible spaces without linear structure. In the absence of examples, the significance of such a generalization is unclear.
scientific article; zbMATH DE number 1375285