A new approach to relatively nonexpansive mappings

Abstract

Abstract. In this paper we study the nonexpansivity of the so-called relatively nonexpansive mappings. A relatively nonexpansive mapping with respect to a pair of subsets (A, B) of a Banach space X is a mapping defined from A ∪ B into X such that T x − T y ≤ x − y for x ∈ A and y ∈ B. These mappings were recently considered in a paper by Eldred et al. (A, B) is nonexpansive. This fact will be used to improve one of the two main results from the aforementioned paper by Eldred et al. At that time we will also obtain several consequences regarding the strong continuity properties of relatively nonexpansive mappings and the relation between the two main results from the same work.

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