A generalization of the Petryshyn-Leggett-Williams fixed point theorem with applications to integral inclusions. (Q1855060)

The authors extend the results of \textit{R. W. Leggett} and \textit{I. R. Williams} [Indiana Univ. Math. J. 28, 673--688 (1979; Zbl 0421.47033)] and \textit{W. V. Petryshyn} [J. Math. Anal. Appl. 124, 237--253 (1987; Zbl 0631.47044)] about the existence of at least three fixed points, to multivalued maps which satisfy an axiomatic index theory. In particular, some criteria for the existence of three nonnegative solutions to integral inclusions are obtained.