On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions
type: Item
instance of: scholarly article
title: On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions
zbMATH Open document ID: 1036.39021
DOI: 10.1016/S0022-247X(02)00181-6
author: Tiberiu Trif
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-12-16T00:00:00Z
review text: General solution of a Jensen type functional equation (in \(n\) variables) is determined for mappings of one real linear space into another. The equation stems from \textit{T. Popoviciu}'s characterization of convex functions via a functional inequality [An. Şti. Univ. Al. I. Cuza Iaşi, N. Ser., Secţ. Ia 11B, 155--164 (1965; Zbl 0166.06303)]. Stability problems for the equation are also considered, following the ideas taken from the papers by \textit{Th. M. Rassias} [Proc. Am. Math. Soc. {72}, 297--300 (1978; Zbl 0398.47040)], \textit{Z. Gajda} [Int. J. Math. Math. Sci. 14, 431--434 (1991; Zbl 0739.39013)] and \textit{P. Găvruţă} [J. Math. Anal. Appl. 184, 431--436 (1994; Zbl 0818.46043)].
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B62
zbMATH DE Number: 1846010
zbMATH Keywords: Jensen type functional equation
zbMATH Keywords: general solution
zbMATH Keywords: stability problem
zbMATH Keywords: convex functions
zbMATH Keywords: Popoviciu's inequality
zbMATH Keywords: linear space
zbMATH Keywords: functional inequality
reviewed by: Bogdan A. Choczewski
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00181-6
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description: scientific article; zbMATH DE number 1846010