convex function


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convex function

[′kän‚veks ′fəŋk·shən]
(mathematics)
A function ƒ(x) is considered to be convex over the interval a,b if for any three points x1, x2, x3 such that a <>x1<>x2<>x3<>b, ƒ (x2)≤ L (x2), where L (x) is the equation of the straight line passing through the points [x1, ƒ(x1)] and [x3, ƒ(x3)].
References in periodicals archive ?
Dr Marjan Praljak from the University of Zagreb, Croatia presented his research paper on positivity of weighted averages of higher order convex function and informed the conference about the results obtained by finding suitable representations of polynomial part and the error term in appropriate form.
Hanson [1] introduced the generalized version of convex function namely invex function.
Let g : C [right arrow] R be a strictly real-valued convex function.
Table 4 shows that when [C.sub.3] is a convex function, the precision and robustness of the algorithm can obtain satisfactory results on [f.sub.1]-[f.sub.5].
A function f : I [subset not equal to] R [right arrow] R is said to be convex function if
Indeed, take a [v.sub.n] [member of] U, supported on [X.sub.n], so that [[parallel][x.sub.n] + [v.sub.n][parallel].sub.n] > [[parallel][x.sub.n][parallel].sub.n] and consider the convex function [h.sub.n](t) = [??][[parallel][x.sub.n] [+ or -] t[v.sub.n][parallel].sub.n].
If [mathematical expression not reproducible] then f([u.sub.1]) is a convex function of [u.sub.1] where [mathematical expression not reproducible] is t- distribution with [n.sub.1] - 1 degrees of freedom.
where the indicator function [i.sub.C] [member of] [[GAMMA].sub.0]([R.sup.n]) : x [member of] [R.sup.n] [right arrow] {0, if x [member of] C; +[infinity], otherwise}, since the total variation term [[parallel]x[parallel].sub.TV] can be represented by a combination of convex function [phi] and linear transformation matrix B; that is, [[parallel]v[parallel].sub.TV] = [phi](Bx).
Moreover, if the fuzzy Hessian matrix [[??].sub.m] is positive semidefinite then, by Theorem 17, the objective function will also be a fuzzy-valued convex function with respect to [less than or equal to]w.