Konvexním

Konvexním is the instrumental singular form of the Czech adjective konvexní, meaning convex. It is used to describe something that has the property of convexity in geometry and related fields. The base adjective konvexní is employed in a range of technical terms, for example konvexní množina (convex set), konvexní funkce (convex function), konvexní tvar (convex shape) and konvexní povrch (convex surface).

In geometry, a set is called convex if for any two points in the set, the line segment joining them lies entirely within the set. This simple criterion implies many useful properties in higher dimensions and underpins various results in analysis and optimization. A convex function is defined on a convex domain and satisfies the inequality f(tx+(1−t)y) ≤ t f(x) + (1−t) f(y) for all x, y in the domain and t in [0, 1]; such functions have a unique global minimum on a convex domain, with numerous applications in economics and engineering.

The instrumental form konvexním typically appears in phrases describing a convex form, surface or shape, such as konvexním tvarem or konvexním povrchem, and is used with masculine inanimate nouns in the appropriate grammatical case. The opposite concept is konkávní (concave). Etymologically, konvexní derives from Latin convexus, borrowed into Czech through historical linguistic contact, and has become standard in mathematical vocabulary.