# concave function

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## concave function

[′kän‚kāv ′fəŋk·shən]
(mathematics)
A function f (x) is said to be concave over the interval a,b if for any three points x1, x2, x3 such that a <>x1<>x2<>x3<>b, f (x2)≥ L (x2), where L (x) is the equation of the straight line passing through the points [x1, f (x1)] and [x3, f (x3)].
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For other given parameters ([alpha], [beta], [lambda], p), the function ~R ([chi]) is a concave function with respect to l.
2] [right arrow] R be a concave function in the variables (y, s), that is, [f.
The U-shaped parabola is obtained not only when the measure of talent used is a concave function (Figures 7 and 8), but also, perhaps, when the function is convex, especially in the case of extremely unbalanced leagues (Figures 5 and 6).
Traditionally, in operations research literatures, the customer's demand is assumed to be decreasing concave function or simply a decreasing linear function with the price as an input variable.
The first two conditions ensure that the probability density function will map a concave function onto another concave function.
F(d) is a convex function then H(d') is a concave function ([[partial derivative].
phi] is said to be a schur concave function on [OMEGA] if and only if -[phi] is schur convex.
Let us also pay attention to the fact that each concave function such that [phi](0) = 0 is subadditive.
b] (*, M, N) is a concave function, whose maximum is attained when ([partial derivative]/[partial derivative]Q)E[[[PI].
Let u: I [right arrow] R be a twice continuously differentiable strictly increasing concave function with decreasing absolute risk aversion defined in an open interval I.
2, that if f is an increasing convex or concave function on [a, b] , then
An example of a concave function is the logarithmic function:

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