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2007 Some remarks on stability and solvability of linear functional equations
Boris Paneah
Banach J. Math. Anal. 1(1): 56-65 (2007). DOI: 10.15352/bjma/1240321555


In the present work we continue studying the solvability of the linear functional equations ${\sum_{j=1}^N }c_j F\circ a_j=H$ and also the strong and weak stability of the corresponding operator $\mathcal{P}$ (see the definition below). By analogy with the Cauchy and Jensen operators once more model operator $\widehat{\mathcal{P}}$ is considered, and the stability problems as well as some solvability problems for $\widehat{\mathcal{P}}$ are studied. Several unsolved problem of a general character are formulated.


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Boris Paneah. "Some remarks on stability and solvability of linear functional equations." Banach J. Math. Anal. 1 (1) 56 - 65, 2007.


Published: 2007
First available in Project Euclid: 21 April 2009

zbMATH: 1130.39026
MathSciNet: MR2350194
Digital Object Identifier: 10.15352/bjma/1240321555

Primary: 39B22
Secondary: 39B52‎

Keywords: a priori estimate , Cauchy operator , Jensen operator , strong , weak and Ulam stability

Rights: Copyright © 2007 Tusi Mathematical Research Group

Vol.1 • No. 1 • 2007
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