Remarks on Strictly Convex and Strictly 2‐Convex 2‐Normed Spaces

Extreme Points and Strict Convexity

“…Note that every linear 2-normed space of dimension 2 and every 2-inner product space are strictly convex ( [6]). Further characterizations of strict convexity in linear 2-normed spaces are given in [l]- [4], [7]- [9], [11] and [12].…”

ON STRICTLY n-CONVEX NORMED LINEAR SPACES

“…Indeed, it is known that if x, y ^ 0, then the relation + 2/|| = ||x|| + ||y|| holds if and only if x = ay for some real a > 0. The strict convexity has been generalized to the space having Property C [3], by which we mean that if ||x + y + z||/3 = ||x|| = ||j/|| = ||z|| = 1, then x,y and z are collinear. A strictly convex space has Property C, but the converse is not generally true ( [3], Example 1).…”

“…The strict convexity has been generalized to the space having Property C [3], by which we mean that if ||x + y + z||/3 = ||x|| = ||j/|| = ||z|| = 1, then x,y and z are collinear. A strictly convex space has Property C, but the converse is not generally true ( [3], Example 1). It is our object in this paper to define a strictly n-convex normed linear space which is a generalization of the above two types of spaces.…”

On Uniformly Convex and Uniformly 2-Convex 2-Normed Spaces

“…: ll (1) X is uniformly 2-convex. Recall that a 2-normed space is said to be strictly 2-convex, if conditions i||x+z,y+z| = 5x,y|| = |y,zj = |z,x||=l imply that z=x+y [4]. It is known that a strictly convex 2-normed space is strictly 2-convex, but not conversely (cf.…”

“…It is known that a strictly convex 2-normed space is strictly 2-convex, but not conversely (cf. [4] Example 2).…”