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

Soon-Mo Jung, Ki-Suk Lee, Michael Th. Rassias and Sung-Mo Yang
Additional contact information
Soon-Mo Jung: Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea
Ki-Suk Lee: Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea
Michael Th. Rassias: Institute of Mathematics, University of Zurich, CH-8057 Zurich, Switzerland
Sung-Mo Yang: Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea

Mathematics, 2020, vol. 8, issue 8, 1-8

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 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 ( s x + t y ) , 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.

Keywords: Hyers-Ulam stability; Hyers-Ulam-Rassias stability; generalized Hyers-Ulam stability; mean value-type functional equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/8/1299/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/8/1299/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:8:p:1299-:d:395167

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().