%0 Journal Article
%T Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces
%A Akachukwu Offia
%A Ugochukwu Osisiogu
%A Theresa Efor
%A Friday Oyakhire
%A Monday Ekhator
%A Friday Nkume
%A Sunday Aloke
%J Open Journal of Optimization
%P 99-108
%@ 2325-7091
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojop.2023.123007
%X In
this paper, we characterize </span><span style=\"font-family:&quot;\">lower semi-continuous pseudo-convex functions</span><span style=\"font-family:&quot;\"> <i>f : X</i> </span><span>¡ú R</span><span style=\"font-family:&quot;\"> &amp;#8746; {+ &amp;#8734;}</span><span style=\"font-family:&quot;\"> </span><span style=\"font-family:&quot;\">on convex
subset of</span><span style=\"font-family:&quot;\"> real Banach spaces <i>K</i> <span>&nbsp;</span>&amp;#8834; <i>X</i> with respect to the pseudo-monotonicity of its</span><span style=\"font-family:&quot;\"> Clarke-Rockafellar Sub-differentia</span><span style=\"font-family:&quot;\">l.</span><span style=\"font-family:&quot;\"> <span style=\"color:black;\">We extend the results on the characterizations of
non-smooth </span>convex functions </span><i><span style=\"font-family:&quot;\">f : X</span></i><span style=\"font-family:&quot;\"> </span><span>¡ú R</span><span style=\"font-family:&quot;\"> &amp;#8746; {+ &amp;#8734;}</span><span style=\"font-family:&quot;\"> on convex subset of</span><span style=\"font-family:&quot;\"> real Banach spaces <i><span>K</span></i><span> <span>&nbsp;</span>&amp;#8834; <i>X</i></span> with <span>respect to the monotonicity of its sub-differentials to the lower
semi-continuo</span>us pseudo-convex functions on real Banach spaces</span><span style=\"font-family:&quot;\">.
%K Real Banach Spaces
%K Pseudo-Convex Functions
%K Pseudo-Monotone Maps
%K Sub-Differentials
%K Lower Semi-Continuous Functions and Approximate Mean Value Inequality
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=127660