Remarks on criteria of prequasi-invex functions

Yang et al gave some criteria of prequasi-invex functions, semistrictly prequasi-invex functions and strictly prequasi-invex functions in 2001, under a certain set of conditions. In this note, some of these conditions can be weakened to get the same results, and another simplified proof for a criterion of prequasi-invex functions established under the condition of lower semicontinuity is given.