Abstract: If  $\alpha ~{\rm and}~\eta $ are  affine in the first argument and skew instead of Condition C, the following results are obtained: (i) if the gradient of a function is (strictly) $\alpha \eta $-pseudomonotone,  the function is (strictly) pseudo $\alpha \eta $-invex;  (ii) if the gradient of a function is quasi $\alpha \eta $-monotone,  the  function is quasi $\alpha \eta $-invex.

Key words: mathematical programming, generalized \alpha \eta -monotonicity, generalized \alpha \eta -invex functions, affine