Fixed point theorems via cone-norms and cone-valued measures of noncompactness

Abstract

In this paper, we obtain an extension of the Krasnoselskii fixed point theorem for sum of two operators to the case of cone normed spaces. We also prove a variant of the Darbo- Sadovskii theorem on fixed points for operators condensing with respect to a cone-valued measure of noncompactness and apply it to the Cauchy problem with deviating argument.