## Abstract In this paper the concepts of strictly convex and uniformly convex normed linear spaces are extended to metric linear spaces. A relationship between strict convexity and uniform convexity is established. Some existence and uniqueness theorems on best approximation in metric linear space
Best Uniform Convex Approximation on a Compact Convex Set
β Scribed by J.T. Chan
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 183 KB
- Volume
- 183
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper, a criterion for which the convex hull of is relatively compact is given when is a relatively compact subset of the space R p of fuzzy sets endowed with the Skorokhod topology. Also, some examples are given to illustrate the criterion.
A convex function \(f\) given on \([-1,1]\) can be approximated in \(L_{r}, 1<p<x\). by convex polynomials \(P_{n}\) of degree at most \(n\) with the accuracy \(o\left(n^{-2 i p}\right)\). This follows from the estimate \(\left\|f-P_{n}\right\|_{p} \leqslant c \cdot n^{-2 / p} \cdot \omega_{2}^{\var
A mountain pass lemma without the PalaisαSmale condition on a closed convex subset of a Banach space is established. Then, we apply it to a semilinear elliptic partial differential equation to obtain one negative solution and a positive solution. Hence we generalize an early result of K.
Let n51 and B52: A real-valued function f defined on the n-simplex D n is approximately convex with respect to We determine the extremal function of this type which vanishes on the vertices of D n : We also prove a stability theorem of Hyers-Ulam type which yields as a special case the best constan