Let f : K := [a, a + [eta] (b, a)] [right arrow] R be a differentiable function
on K[degrees] (the interior of K) and a, b [member of] K[degrees] with a < a + [eta] (b, a).
For any differentiable function
h satisfying E[[absolute value of h'(X)]] < [infinity], we have
alpha]) to be a differentiable function
nor a single value mapping (thus allowing for multiple solutions).
We still assume that f is a twice differentiable function
in [OMEGA] satisfying f"([x.
z]) are given n-times differentiable functions
in some closed domain D.
Let w [member of] I be a simple zero of sufficiently differentiable function
f : I [?
Pratt (1964) suggests a formula for comparing two agents' risk aversion: Agent A is more risk averse than agent B if there exists an increasing, strictly concave, and twice differentiable function
|Phi~ such that |U.
15]) Let f: X [right arrow] R be a differentiable function
on a nonempty closed convex subset X of [R.
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be two Riemannian manifolds and f a positive differentiable function
2]), where [PHI] = [PHI] (u) is a differentiable function
of its variable u = [[absolute value of z].
d] and 0 < q [less than or equal to] + [infinity], if there exists an infinitely differentiable function
[eta] satisfying [eta]([xi]) = 1 if [absolute value of [xi]] [less than or equal to] [rho] and [eta]([xi]) = 2[rho] for some 0 < p < 1/2 such that jz([eta]v)/w) belongs to [L.
n]: I [right arrow] K be given continuous functions, let g: I [right arrow] X be a given continuous function, and let y: I [right arrow] X be any n times continuously differentiable function
satisfying the inequality
d], * an infinitely differentiable function
with support in the unit ball such that [DELTA] [phi](x)dx = 1 and a positive real number.
Instead, the physicists' potential energy function (differentiable with respect to particle position components) suggested to economists that they should make Bentham's utility a differentiable function
of consumer good quantities.
Assume the function f: R [right arrow] R is a differentiable function
and g : T [right arrow] R is a delta- differentiable function