Application of the omitted ray fixed point theorem

Abstract

This paper presents a nontrivial application of the omitted ray fixed point theorem. Existence of solutions arguments to nonlinear boundary value problems utilizing the Krasnoselskii fixed point theorem, Leggett-Williams fixed point theorem and their functional generalizations are characterized by mapping portions of an inward boundary inward and portions of an outward boundary outward. In this application we demonstrate a technique that avoids requiring any portion of the inward boundary being mapped inward using the omitted ray fixed point theorem.

Keywords

• fixed-point theorems
• omitted ray
• altman
• leggett-williams