An application of KKM-map principle.
We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.
An extension of Kirk - Schöneberg surjectivity result is established.
We obtain necessary conditions for convergence of the Cauchy Picard sequence of iterations for Tricomi mappings defined on a uniformly convex linear complete metric space.
In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.