Fixed points of asymptotically regular mappings in spaces with uniformly normal structure

@inproceedings{GrnickiFixedPO,
title={Fixed points of asymptotically regular mappings in spaces with uniformly normal structure},
author={Jaros law G{\'o}rnicki}
}

It is proved that: for every Banach space X which has uniformly normal structure there exists a k > 1 with the property: if A is a nonempty bounded closed convex subset of X and T : A → A is an asymptotically regular mapping such that lim inf n→∞ |||T n ||| < k, where |||T ||| is the Lipschitz constant (norm) of T , then T has a fixed point in A.