A differentiable function is said to be invex if there exists a function such that, for all
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 -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.