On the super fixed point property in product spaces

Abstract

We prove that if F is a finite-dimensional Banach space and X has the super fixed point property for nonexpansive mappings, then F ⊕ X has the super fixed point property with respect to a large class of norms including all l p norms, 1 p < ∞. This provides a solution to the "super-version" of the problem of Khamsi (1989).

New geometric constants of isosceles orthogonal type

“…The concept of normal structure has always been a research hotspot because it is closely related to the fixed point theory. It plays an important role in studying the geometric properties and applications of target space (see [14,24,25]). Next, we will use the constant L J (X) to describe whether space X has normal structure.…”

Hyper-extensions in metric fixed point theory

“…Recently, a few general fixed point theorems in direct sums were proved in [31,32] (see also [24,30]). Although their proofs were formulated in standard terms, the original ideas came from nonstandard analysis.…”

The fixed point property inJB∗-triples and preduals ofJBW∗-triples

“…Thus the strengthenings of the FPP and the NS which were introduced in [44] and [31] and called, respectively, the super fixed point property and super normal structure, are equivalent to the usual FPP in the settings of JB * -triples and preduals of JBW * -triples (Theorem 4.2). As a consequence, every reflexive, real or complex, JB * -triple or the predual of a JBW * -triple, has uniform normal structure (Corollary 4.3).…”