A fixed point theorem for asymptotically regular mappings
Let C be a closed, bounded, convex subset of a Hilbert space. Let T : C → C be a demicontinuous pseudocontraction. Then T has a fixed point. This is shown by a combination of topological and combinatorial methods.
A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject
A fixed point theorem is proved for non-self multi-valued mappings in a metrically convex complete metric space satisfying a slightly stronger contraction condition than in Rhoades [3] and under a weaker boundary condition than in Itoh [2] and Rhoades [3].
In this paper, we will give a new fixed point theorem for lower semicontinuous multimaps in a Hausdorff topological vector space.