The Bregman distance without the Bregman function. II
A weak-strong space is defined as a tuple \((X,S,\mathbb{T},d)\) consisting of a metric space \((X,d)\), a nonempty set \(S\subseteq X\), and a topology \(\mathbb{T}\) on \(X\) related to the metric topology in a suitable way. An instance of a weak-strong space is a reflexive Banach space together with its weak topology and a convex subset. In the context of weak-strong spaces, the author defines an abstract notion of Bregman distance in an axiomatic way, thus not relying upon any given Bregman function, and introduces appropriate notions of asymptotic fixed points and strong nonexpansiveness for mappings \(T:S\longrightarrow S\). The main theorem is a convergence result to a common asymptotic fixed point of a finite collection of strongly nonexpansive mappings.NEWLINENEWLINEEditorial remark. Part I has appeared as [\textit{D. Reem}, ``The Bregman distance without the Bregman function'', preprint].NEWLINENEWLINEFor the entire collection see [Zbl 1241.00017].
scientific article; zbMATH DE number 6077534