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Outer \(\gamma\)-convex functions on a normed space. (English) Zbl 1083.26010

This paper deals with the notion of outer \(\gamma\)-convexity introduced by Hoang Xuan Phu and the author [Vietnam J. Math. 27, No. 4 , 323–334 (1999; Zbl 0964.46005)]. Properties of outer \(\gamma\)-convex sets and outer \(\gamma\)-convex functions are given; for instance, for fourth degree polynomials of one variable outer \(\gamma\)-convexity is characterized in terms of their coefficients. The relationship between outer \(\gamma\)-convexity of a function and that of its epigraph is also analyzed.

MSC:

26B25 Convexity of real functions of several variables, generalizations
52A41 Convex functions and convex programs in convex geometry
26A51 Convexity of real functions in one variable, generalizations

Citations:

Zbl 0964.46005
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