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

Smaïl Djebali, Karima Mebarki

DOI: http://dx.doi.org/10.12775/TMNA.2019.055

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.

Keywords


Index; fixed point; k-set contraction; expansive mapping; Krasnosel'skii's Theorem; compression and expansion

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