Generalized convex functions on normal decomposition systems.

In this paper, the class of weakly ψ -uniformly convex functions is introduced and studied. Such functions are defined on a convex subcone D of a linear space V endowed with the structure of a normal decomposition system (V , G , (·) ↓) . In particular, superquadratic functions and c-strongly convex functions are recovered as special cases. Some results in Abramovich et al. (J Math Anal Appl 327: 1444–1460, 2007), intended for multidimensional superquadratic functions defined on R + m , are extended to the case of weakly ψ -uniformly convex functions. The concept of ψ -almost superadditivity of functions is presented and applied. Interpretations of the obtained results are demonstrated for some matrix normal decomposition systems. [ABSTRACT FROM AUTHOR]