We 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.
Moosaei, M. (2016). On fixed points of fundamentally nonexpansive mappings in Banach spaces. International Journal of Nonlinear Analysis and Applications, 7(1), 219–224. https://doi.org/10.22075/ijnaa.2015.308
MLA
Moosaei, M. "On fixed points of fundamentally nonexpansive mappings in Banach spaces", International Journal of Nonlinear Analysis and Applications, 7, 1, 2016, 219–224. doi: 10.22075/ijnaa.2015.308
HARVARD
Moosaei, M. (2016). 'On fixed points of fundamentally nonexpansive mappings in Banach spaces', International Journal of Nonlinear Analysis and Applications, 7(1), pp. 219–224. doi: 10.22075/ijnaa.2015.308
CHICAGO
Moosaei, M., "On fixed points of fundamentally nonexpansive mappings in Banach spaces." International Journal of Nonlinear Analysis and Applications, 7 1 (2016): 219–224, doi: 10.22075/ijnaa.2015.308
VANCOUVER
Moosaei M. On fixed points of fundamentally nonexpansive mappings in Banach spaces. IJNAA. 2016;7(1):219–224. doi: 10.22075/ijnaa.2015.308
International Journal of Nonlinear Analysis and Applications