A Characterization of Extremal Sets in Hilbert Spaces
We give a characterization of extremal sets in Hilbert spaces that generalizes a classical theorem of H. W. E. Jung. We investigate also the behaviour of points near to the circumsphere of such a set with respect to the Kuratowski and Hausdorff measures of non-compactness.
N ov 2 00 4 A Note on Self-extremal Sets in L p ( Ω ) Spaces by
In [5], [6] we introduced the notion of (self-) extremal sets of a Banach space (X, ‖ · ‖). For a non-empty bounded subset A of X we denote by r(A) the relative Chebyshev radius of A with respect to the closed convex hull coA of A, i.e. r(A) := inf y∈coA sup x∈A ‖x−y‖. The self-Jung constant of X is defined by Js(X) : = sup {r(A) : A ⊂ X, with diam(A) = 1}. If in this definition we replace r(A) by the relative Chebyshev radius rX(A) of A with respect to the wholeX , we get the Jung constant J(X) ofX . Recall that a bounded subset A ofX consisting of at least two points is said to be extremal (resp. self-extremal) if rX(A) = J(X) d(A) (resp. r(A) = Js(X) d(A)).
Existence of nonoscillatory solutions of Higher order neutral differential equations
This article is concerned with nonoscillatory solutions of higher order nonlinear neutral differential equations with deviating and distributed deviating arguments. By using Knaster-Tarski fixed point theorem, new sufficient conditions are established. Illustrative example is given to show applicability of results.