Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II

Autor:	Soon-Mo Jung, Ki-Suk Lee, Michael Th. Rassias, Sung-Mo Yang
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	Hyers-Ulam stability Hyers-Ulam-Rassias stability generalized Hyers-Ulam stability mean value-type functional equation Mathematics QA1-939
Zdroj:	Mathematics, Vol 8, Iss 8, p 1299 (2020)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math8081299
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)−g(y)=(x−y)h(sx+ty), where f,g,h:X→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:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/b5d9c09820d94c96b3d2f7748e971e69 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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