Common fixed point theorems for nonexpansive mappings using the lower semicontinuity property
Volume 154 / 2018
Colloquium Mathematicum 154 (2018), 157-165
MSC: Primary 47H10; Secondary 46B20, 47H09.
DOI: 10.4064/cm7216-5-2017
Published online: 23 August 2018
Abstract
Suppose that $E$ is a Banach space, $\tau $ a topology under which the norm of $E$ becomes $\tau $-lower semicontinuous and $\mathcal {S}$ a commuting family of $\tau $-continuous nonexpansive mappings defined on a $\tau $-compact convex subset $C$ of $E.$ It is shown that the set of common fixed points of $\mathcal {S}$ is a nonempty nonexpansive retract of $C$. Along the way, a few other related fixed point theorems are derived.
