Fixed points of multivalued maps in modular function spaces (Q1030599)

Let \(L_\rho\) be a modular function space in the sense of Kozlowski, generated by a modular \(\rho\), and let \(C\) be a nonempty, \(\rho\)-closed subset of \(L_\rho\). Let \({\mathcal C}(C)\) be the collection of all nonempty, \(\rho\)-closed subsets of \(C\). It is proved that if \(T:C\to {\mathcal C}(C)\) is a \(\rho\)-contractive-type (or weakly \(\rho\)-contractive-type) map, then \(T\) has a fixed point.