Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68227120160305On fixed points of fundamentally nonexpansive mappings in Banach spaces21922430810.22075/ijnaa.2015.308ENMohammadMoosaeiDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, IranJournal Article20150128We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex.https://ijnaa.semnan.ac.ir/article_308_db07694ccc7a387cc590bac3f64bd749.pdf