Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II
| Autor: | Michael Th. Rassias, Ki-Suk Lee, Soon-Mo Jung, Sung-Mo Yang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Normed algebra General Mathematics lcsh:Mathematics 010102 general mathematics Mean value Hyers–Ulam–Rassias stability lcsh:QA1-939 01 natural sciences generalized Hyers-Ulam stability Norm (mathematics) 0103 physical sciences Computer Science (miscellaneous) mean value-type functional equation Hyers-Ulam stability 010307 mathematical physics Hyers-Ulam-Rassias stability 0101 mathematics Engineering (miscellaneous) Commutative property Mathematics |
| Zdroj: | Mathematics, Vol 8, Iss 1299, p 1299 (2020) Mathematics Volume 8 Issue 8 |
| ISSN: | 2227-7390 |
| Popis: | Let X be a commutative normed algebra with a unit element e (or a normed field of characteristic different from 2), where the associated norm is sub-multiplicative. We prove the generalized Hyers-Ulam stability of a mean value-type functional equation, f(x)&minus g(y)=(x&minus y)h(sx+ty), where f,g,h:X&rarr X are functions. The above mean value-type equation plays an important role in the mean value theorem and has an interesting property that characterizes the polynomials of degree at most one. We also prove the Hyers-Ulam stability of that functional equation under some additional conditions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|