Krasnoselskii-type results for equiexpansive and equicontractive operators with application in radiative transfer equations

Abstract

In this paper, we study the results of fixed points for the operator equations of type $ x = H(\digamma x, x) $ using the idea of measure of noncompactness and assuming that the operator $ \digamma $ is $ k $ -set contractive (strictly $ k $ -set contractive, or a continuous) and the family $ \{H(u, .):u\} $ is equiexpansive or equicontractive. The obtained results are generalization of Krasnoselskii type fixed point results. Some examples are given to elaborate new concepts. We use the main result to find the existence of solutions for the stationary radiative transfer equation in a channel. We demonstrate our theory with an example by comparison of an approximate solution with the exact solution.

Keywords

• krasnoselskii
• equiexpansive
• equicontractive
• fixed points
• radiative transfer