The notions of quasiconvexity, Wright convexity and convexity for functions defined on a metric Abelian group are introduced. Various characterizations of such functions, the structural properties of the functions classes so obtained are established and several well-known results are extended to this new setting.

中文翻译：

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在度量阿贝尔群上定义的函数的凸性

介绍了在度量阿贝尔群上定义的函数的拟凸，怀特凸和凸的概念。建立了此类功能的各种特性，所获得的功能类别的结构特性，并将一些众所周知的结果扩展到了这一新设置。