Abstract
We show that each uniformly continuous quasiconvex function defined on a subspace of a normed space X X admits a uniformly continuous quasiconvex extension to the whole X X with the same “invertible modulus of continuity”. This implies an analogous extension result for Lipschitz quasiconvex functions, preserving the Lipschitz constant. We also show that each uniformly continuous quasiconvex function defined on a uniformly convex set A ⊂ X A\subset X admits a uniformly continuous quasiconvex extension to the whole X X . However, our extension need not preserve moduli of continuity in this case, and a Lipschitz quasiconvex function on A A may admit no Lipschitz quasiconvex extension to X X at all.
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.
