Author(s)

Akachukwu Offia^1*, Ugochukwu Osisiogu², Theresa Efor², Friday Oyakhire¹, Monday Ekhator¹, Friday Nkume¹, Sunday Aloke³

¹Department of Mathematics and Statistics, Alex Ekwueme Federal University, Ndufu-Alike, Nigeria.
²Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Nigeria.
³Department of Industrial Mathematics, David Umahi Federal University of Health Sciences, Uburu, Nigeria.

In this paper, we characterize lower semi-continuous pseudo-convex functions f : 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.

Real Banach Spaces, Pseudo-Convex Functions, Pseudo-Monotone Maps, Sub-Differentials, Lower Semi-Continuous Functions and Approximate Mean Value Inequality

Offia, A. , Osisiogu, U. , Efor, T. , Oyakhire, F. , Ekhator, M. , Nkume, F. and Aloke, S. (2023) Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces. Open Journal of Optimization, 12, 99-108. doi: 10.4236/ojop.2023.123007.