Fixed point theorems for upper semicontinuous multivalued operators in locally convex spaces

In the paper, we will discus some τ-topological properties of the set F(S0,T,H) := {x ∈ X : S0x ∈ Tx + Hx}, where T is multivalued operator, S0 and H are two single valued operators acting on a Hausdorff locally convex space X and τ is a weaker Hausdorff locally convex topology on X. Moreover, when X is a τ-angelic space with the so-called τ-Krein-Šmulian property, we will provide some new variants of fixed point theorems for multivalued operators. Our results are formulated in terms of τ-upper semicontinuity, τ-S0-demicom-pactness and families of axiomatic measures of noncompactenss.