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http://dx.doi.org/10.4134/BKMS.2008.45.1.133

STABILITY OF THE MULTI-JENSEN EQUATION  

Prager, Wolfgang (INSTITUT FUR MATHEMATIK AND WISSENSCHAFTLICHES RECHNEN KARL-FRANZENS UNIVERSITY GRAZ)
Schwaiger, Jens (INSTITUT FUR MATHEMATIK AND WISSENSCHAFTLICHES RECHNEN KARL-FRANZENS UNIVERSITY GRAZ)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 133-142 More about this Journal
Abstract
Given an $m{\in}\mathbb{N}$ and two vector spaces V and W, a function f : $V^m{\rightarrow}W$ is called multi-Jensen if it satisfies Jensen's equation in each variable separately. In this paper we unify these m Jensen equations to obtain a single functional equation for f and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.
Keywords
stability; multi-Jensen functions;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 8  (Related Records In Web of Science)
Times Cited By SCOPUS : 8
연도 인용수 순위
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2 S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Co., Inc., River Edge, NJ, 2002
3 G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190   DOI
4 W. Prager and J. Schwaiger, Multi-affine and multi-Jensen functions and their connection with generalized polynomials, Aequationes Math. 69 (2005), no. 1-2, 41-57   DOI