On a measure of noncompactness in the Holder space Ck,γ(Ω) and its application

In this article, based on the concept of relative compactness in the Holder space Ck,γ(Ω) where k≥0, γ∈(0,1] and Ω is a compact subset of RN, we present a new measure of noncompactness on Ck,γ(Ω). Moreover, as an application we study the existence of solution of a nonlinear integral equation in the Holder space by applying Darbo fixed point theorem.