In
this paper, we characterize lower semi-continuous pseudo-convex functionsf : X→ R ∪ {+ ∞}on convex
subset of real Banach spaces K？⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential.We extend the results on the characterizations of
non-smooth convex functions f : X→ R ∪ {+ ∞} on convex subset of real Banach spaces K？⊂ X with respect to the monotonicity of its sub-differentials to the lower
semi-continuous pseudo-convex functions on real Banach spaces.
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