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.
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