Some fixed point theorems for s-convex subsets in p-normed spaces based on measures of noncompactness

Abstract

The Kurotowskii and Hausdorff measures of noncompactness in p-normed spaces are studied, where $$0<p\le 1$$ . By metric retraction and calculation of measures of noncompactness, some fixed point theorems for s-convex subsets are proved, with respect to single-valued and set-valued condensing operators, where $$0<s\le p$$ . The results herein extend and generalize some of the well-known fixed point theorems, such as the types of Darbo, Sadovski, Leray-Schauder, and Martelli.