# convex function

(redirected from Logarithmically convex)

## 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 ?
Some new generalized concepts in this point of view are quasiconvex [1], strongly convex [2], approximately convex [3], logarithmically convex [4], midconvexfunctions [5], pseudoconvex [6], [phi]-convex [7], [lambda]-convex [8], h-convex [9], delta-convex [10], Schur convex [11-15], and others [16-19].
which implies that the function [[gamma].sup.(m).sub.q](x,z) is logarithmically convex. Also, since [[gamma].sup.(0).sub.q](x, z) = [[gamma].sub.q](x, z), then it follows that [[gamma].sub.q](x, z) is also logarithmically convex.
Srivastava, "Alternative proofs for monotonic and logarithmically convex properties of one-parameter mean values," Applied Mathematics and Computation, vol.
First we recall some definitions and facts about exponentially convex and logarithmically convex functions (see, e.g., [13,14] or [9]) which we need for our results.
(a) [GAMMA] is a logarithmically convex function (i.e.
The function f given by (15) is strictly logarithmically convex on (0, [infinity]) for k [greater than or equal to] 1.
is strictly decreasing and strictly logarithmically convex on (0, [infinity]).

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