Delta-points in Banach spaces generated by adequate families
نویسندگان
چکیده
We study delta-points in Banach spaces hA,p generated by adequate families A, where 1≤p<∞. When p>1, we prove that neither nor its dual contain delta-points. Under the extra assumption A is regular, same true when p=1. In particular, Schreier and their duals fail to have If consists only of finite sets, are able rule out existence hA,1 Daugavet-points dual. also show if polyhedral, then it either (I)-polyhedral or (V)-polyhedral (in sense Fonf Veselý).
منابع مشابه
Nearest Points and Delta Convex Functions in Banach Spaces
Given a closed set C in a Banach space (X, ‖ · ‖), a point x ∈ X is said to have a nearest point in C if there exists z ∈ C such that dC(x) = ‖x − z‖, where dC is the distance of x from C. We shortly survey the problem of studying the size of the set of points in X which have nearest points in C. We then turn to the topic of delta-convex functions and indicate how it is related to finding neare...
متن کاملOn Best Proximity Points in metric and Banach spaces
Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed...
متن کاملOn fixed points of fundamentally nonexpansive mappings in Banach spaces
We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...
متن کاملNew iteration process for approximating fixed points in Banach spaces
The object of this paper is to present a new iteration process. We will show that our process is faster than the known recent iterative schemes. We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings. We also present a numerical example for proving the rate of convergence of our res...
متن کاملCommon Fixed Points in Ordered Banach Spaces
In [1] Dhage, O’Regan and Agarwal introduced the class of weak isotone mappings and the class of countably condensing mappings in an ordered Banach space and they prove some common fixed point theorems for weak isotone mappings. In this paper we introduce the notion of g-weak isotone mappings which allows us to generalize some common fixed point theorems of [1]. We recall the definition of orde...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2022
ISSN: ['1945-6581', '0019-2082']
DOI: https://doi.org/10.1215/00192082-10123638