Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II
- Authors
- Jung, Soon-Mo; Lee, Ki-Suk; Rassias, Michael Th.; Yang, Sung-Mo
- Issue Date
- Aug-2020
- Publisher
- MDPI
- Keywords
- Hyers-Ulam stability; Hyers-Ulam-Rassias stability; generalized Hyers-Ulam stability; mean value-type functional equation
- Citation
- MATHEMATICS, v.8, no.8, pp.1 - 8
- Journal Title
- MATHEMATICS
- Volume
- 8
- Number
- 8
- Start Page
- 1
- End Page
- 8
- URI
- https://scholarworks.bwise.kr/hongik/handle/2020.sw.hongik/11615
- DOI
- 10.3390/math8081299
- ISSN
- 2227-7390
- Abstract
- Let X be a commutative normed algebra with a unit element e (or a normed field of characteristic different from 2), where the associated normis 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 theHyers-Ulamstability of that functional equation under some additional conditions.
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