Phan Thanh An Outer \(\gamma\)-convex functions on a normed space. (English) Zbl 1083.26010 JIPAM, J. Inequal. Pure Appl. Math. 6, No. 3, Paper No. 85, 8 p. (2005). 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. Reviewer: Juan-Enrique MartĂnez-Legaz (Barcelona) 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 Keywords:generalized convexity; Jensen inequality; epigraph Citations:Zbl 0964.46005 PDFBibTeX XMLCite \textit{Phan Thanh An}, JIPAM, J. Inequal. Pure Appl. Math. 6, No. 3, Paper No. 85, 8 p. (2005; Zbl 1083.26010) Full Text: EuDML