9 citations · 10 across the 3 of their papers we have counts for
6 papers
On extremal nonexpansive mappings
Christian Bargetz, Michael Dymond, Katriin Pirk
We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometr…
On generic convergence of successive approximations of mappings with convex and compact point images
Christian Bargetz, Emir Medjic, Katriin Pirk
We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with conv…
Stability of diametral diameter two properties
Johann Langemets, Katriin Pirk
We prove that the diametral diameter two properties are inherited by -ideals (e.g., -ideals). On the other hand, these properties are lifted from an -ideal to the superspa…
Daugavet- and Delta-points in absolute sums of Banach spaces
Rainis Haller, Katriin Pirk, Triinu Veeorg
A Daugavet-point (resp.~-point) of a Banach space is a norm one element for which every point in the unit ball (resp.~element itself) is in the closed convex hull of uni…
Delta- and Daugavet-points in Banach spaces
Trond Arnold Abrahamsen, Rainis Haller, Vegard Lima +1
A -point of a Banach space is a norm one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance from . If,…
Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm
Rainis Haller, Katriin Pirk, Märt Põldvere
We prove that the diametral strong diameter 2 property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has a…