TY - JOUR
AU - Radhakrishnan, M.
AU - Rajesh, S.
PY - 2019/04/01
Y2 - 2024/02/25
TI - Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 20
IS - 1
SE -
DO - 10.4995/agt.2019.10360
UR - https://polipapers.upv.es/index.php/AGT/article/view/10360
SP - 119-133
AB - <p>Kirk introduced the notion of pointwise eventually asymptotically non-expansive mappings and proved that uniformly convex Banach spaces have the fixed point property for pointwise eventually asymptotically non expansive maps. Further, Kirk raised the following question: “Does a Banach space X have the fixed point property for pointwise eventually asymptotically nonexpansive mappings when ever X has the fixed point property for nonexpansive mappings?”. In this paper, we prove that a Banach space X has the fixed point property for pointwise eventually asymptotically nonexpansive maps if X has uniform normal structure or X is uniformly convex in every direction with the Maluta constant D(X) < 1. Also, we study the asymptotic behavior of the sequence {T<sup>n</sup>x} for a pointwise eventually asymptotically nonexpansive map T defined on a nonempty weakly compact convex subset K of a Banach space X whenever X satisfies the uniform Opial condition or X has a weakly continuous duality map.</p>
ER -