A CHARACTERIZATION OF STRICTLY CONVEX LINEAR 2-NOBMED SPACES

Abstract

In this note we extend the concept of best approximation to linear 2-normed spaces. We define proxi-minal, semi-Chebyshev, and Chebyshev sets in linear 2-normed spaces. A linear 2-normed space X is said to be strictly convex if for all X,Y,Z, ϵ x, ||x+y.z|| = ||x,z|| + y,z||, ||x,y|| = 1 and z ϵ. V (x.u) imply x = y. We prove tat a linear 2-normed space X is strictly convex if and only if all convex sets in X are semi-Chebyshev.