*(English)*Zbl 0731.26009

A differentiable function $f:{\mathbb{R}}^{n}\to \mathbb{R}$ is said to be invex if there exists a function $\eta (y,x)\in {\mathbb{R}}^{n}$ such that, for all $y,x\in {\mathbb{R}}^{n}$

Various extensions of such functions including pseudo- and quasi-invex have been defined and their relationship to each other and other generalizations of convexity have been studied. For the non- differentiable case, f is said to be pre-invex if

This comprehensive paper brings together many of these scattered results which are then studied, compared, and extended. Some definitions that are introduced include $\eta $-invex subsets, pseudo and quasi-pre-invex functions. One very minor correction. Reference 2 should be to the Journal, not the Bulletin, of the Australian Mathematical Society.