Abstract
AbstractIn this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation:f(x1+⋯+xl)=(l−1)f(x1+⋯+xl−1l−1)+f(xl)for a fixed integerlwithl>1, and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.MSC:39B52, 54C60, 91B44.
Highlights
Introduction and preliminariesThe theory of set-valued functions has been much related to the control theory and the mathematical economics
The stability problem of functional equations originated from a question of Ulam [ ] concerning the stability of group homomorphisms
The stability problems of several functional equations have been extensively investigated by a number of authors, and there are many interesting results concerning this problem
Summary
Introduction and preliminariesThe theory of set-valued functions has been much related to the control theory and the mathematical economics. The stability problems of several functional equations have been extensively investigated by a number of authors, and there are many interesting results concerning this problem (see [ – ]). Let (Ccb(Y ), ⊕, h) be endowed with the Hausdorff distance h.
Sign-in/Register to view highlights & summary 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.
