Fixed point theory for \(k\)-CAR sets (Q1589941)

If \(E\) is a Fréchet space, then a subset \(A\) of \(E\) is said to be \(k\)-CAR if there exists a continuous \(k\)-set contractive retraction from \(\overline{\text{conv}} A\) to \(A\). Fixed point results for upper semicontinuous self-multivalued operators between \(k\)-CAR sets, Leray-Schauder type principles for u.s.c. multifunctions \(F:\overline U\to 2^C\) having nonempty values (where \(C\) is a \(k\)-CAR set and \(U\) is open in \(C\)) and a fixed point theorem of Furi-Pera type for upper semicontinuous multifunctions are the main targets of this paper.