Abstract
The class of convex sets plays a central role in the theory. The subset C of the normed space X is said to be convex if $$t\in\, (0 , 1)\,,\:\:\: x , y\: \in \:C\:\: \Longrightarrow\:\: (1-t) x+ t y\: \in \:C\,.$$ The separation of convex sets is the issue treated by the celebrated Hahn-Banach theorem, often said to be the most basic tool of classical functional analysis. We also study convex functions, a more modern consideration. Such functions, which turn out to have special regularity properties, will play a big role in things to come. We also introduce lower semicontinuous and extended-valued functions, which are important later in optimization. Support functions and indicator functions are important examples of these.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
