Abstract
The paper is devoted to a new unidirectional mean value inequality for the Fréchet subdifferential of a continuous function. This mean value inequality finds an intermediate point and localizes its value both from above and from below; for this reason, the inequality is called two-sided. The inequality is considered for a continuous function defined on a Fréchet smooth space. This class of Banach spaces includes the case of a reflexive space and the case of a separable Asplund space. As some application of these inequalities, we give an upper estimate for the Fréchet subdifferential of the upper limit of continuous functions defined on a reflexive space.
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.
