Kartsatos, Athanassios G. (ed.), Theory and applications of nonlinear operators of accretive and monotone type. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 178, 313-318 (1996).
Let be a reflexive Banach space, and let be a convex continuous functional which is Gǎteaux differentiable. The Bregman distance corresponding to is defined by For a selfmapping of a convex set denote by the set of its asymptotic fixed points. is said to be strongly nonexpansive (with respect to a nonempty ) if for all and and if implies for any and bounded sequence .
The main result states the following. If are strongly nonexpansive self-mappings of a convex set , the intersection of as well as are nonempty and is weakly sequentially continuous then the weak
exists for each and belongs to .
Applications to convex sets intersection problem and to finding a common zero of finitely many monotone operators are given.