## On approximately convex functions.(English)Zbl 0823.26006

Let $$D$$ be a convex subset of a real vector space $$X$$ and $$\varepsilon$$ a nonnegative constant. A real valued function $$f$$ on $$D$$ is $$\varepsilon$$- convex if $$f(tx+ (1- t)y)- tf(x)- (1- t) f(y)\leq \varepsilon$$ and $$\varepsilon$$-Wright-convex if $$f(tx+ (1- t)y)+ f((1- t)x+ ty)- f(x)- f(y)\leq 2\varepsilon$$ $$(x, y\in [0, 1])$$. A typical result states that $$\varepsilon$$-Wright-convex functions, bounded from below on a neighbourhood of an interior point of $$D$$, are $$2\varepsilon$$-convex.

### MSC:

 26A51 Convexity of real functions in one variable, generalizations 26B25 Convexity of real functions of several variables, generalizations 39B72 Systems of functional equations and inequalities
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### References:

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