Fixed point index theory for perturbation of expansive mappings by $k$-set contractions

Abstract

In this work, we develop a fixed point index theory for the sum of $k$-set contractions and expansive mappings with constant $h> 1$ when $0\le k< h-1$ as well as in the limit case $k=h-1$. After computing this new index, several fixed point theorems and recent results are derived, including Krasnosel'skii type theorems. Two examples of application illustrate the theoretical results.