Fixed point theorems for nonexpansive mappings and Suzuki-generalized nonexpansive mappings on a Banach lattice - S. Dhompongsa (2018)
We prove the existence of fixed points for multivalued nonexpansive nonself-mappings on a weakly orthogonal reflexive Banach lattice with uniformly monotone norm. Moreover, for single-valued mappings, we extend Betiuk-Pilarska and Prus's result [A. Betiuk-Pilarska, S. Prus, Banach lattices which are order uniformly noncreasy, J. Math. Anal. Appl. 342 (2008) 1271-1279] on the weak fixed point property to continuous mappings satisfying condition (C) on a w-weakly orthogonal OUNC Banach lattice. © 2009 Elsevier Ltd. All rights reserved.