Sentence examples for be a convex mapping from inspiring English sources

Let f : I ⊆ R → R be a convex mapping and a, b ∈ I with a < b.

Let be a convex mapping defined on the interval of real numbers and, with, then.

Let (f: I subseteqmathbb{R}rightarrowmathbb{R}) be a convex mapping and (a, b in I) along with (a < b).

Let C be a convex subset of the real linear space X and let f : C → R be a convex mapping.

The non-negative real numbers and the positive real numbers are denoted by (mathbb {R}_{0}=[0,infty)) and (mathbb{R}_= 0,infty)), respectively. Let (f : I subseteqmathbb{R}rightarrowmathbb{R}) be a convex mapping defined on the interval I of real numbers and (a, b in I) with (a < b).

For, the invex set is a convex set and the -preinvex mapping is a convex mapping.

If in addition, is a convex mapping, then conversely, solves (GVVIP) which implies that solves (GVUOP).

Thus, for example, we know that if (f"(x)>0) for all x in the domain of f, then f is a convex mapping, whereas if (f"(x)<0) on the domain of f, then f is a concave mapping.

As such, by definition we recover immediately that y is a convex map.

Then (Delta^{2}y(t)>0) for each (tinmathbb{N}_{a}) if and only if y is a convex map on (mathbb{N}_{a}).

If all this is so and also (Delta_{0}^{mu}y(t)) is nonnegative, then we may deduce that (Delta^{2}y(t)ge0); in fact, if (Delta_{0}^{mu}y(t)) is positive, then we can actually deduce that y is a convex map - i.e., that (Delta^{2}y(t)>0).