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  1. TheIf you throw in positive homogeneity, then the first class of functions is what is called sublinear, see for instance Proposition 1.1.4 (Convex functions;"Fundamentals of Convex Analysis"; Hiriart-Urruty, Claude Lemaréchal).

  2. The second class of functions that you mention is essentially the same as the Wright convex functions, see for instance pg. 223 of A.W. Roberts, D.E. Varberg, "Convex functions", Academic Press, 1973.

  1. The first class of functions is called sublinear, see for instance Proposition 1.1.4 (Convex functions; Hiriart-Urruty, Claude Lemaréchal).

  2. The second class of functions that you mention is essentially the same as the Wright convex functions, see for instance pg. 223 of A.W. Roberts, D.E. Varberg, "Convex functions", Academic Press, 1973.

  1. If you throw in positive homogeneity, then the first class of functions is what is called sublinear, see for instance Proposition 1.1.4 ("Fundamentals of Convex Analysis"; Hiriart-Urruty, Claude Lemaréchal).

  2. The second class of functions that you mention is essentially the same as the Wright convex functions, see for instance pg. 223 of A.W. Roberts, D.E. Varberg, "Convex functions", Academic Press, 1973.

Source Link
Suvrit
Suvrit
  • 28.6k
  • 7
  • 82
  • 150

  1. The first class of functions is called sublinear, see for instance Proposition 1.1.4 (Convex functions; Hiriart-Urruty, Claude Lemaréchal).

  2. The second class of functions that you mention is essentially the same as the Wright convex functions, see for instance pg. 223 of A.W. Roberts, D.E. Varberg, "Convex functions", Academic Press, 1973.