On order-Lipschitz mappings in Banach spaces without normalities of involving cones

Abstract

We prove a new fixed point theorem of order-Lipschitz mappings in Banach spaces without assumption of normalities of the involving cones, which presents a positive answer to a problem raised in [S. Jiang, Z. Li, Fixed Point Theory Appl., 2016 (2016), 10 pages] and improves the corresponding results of Krasnoselskii and Zabreiko's and Zhang and Sun's since the normality of the involving cone is removed.