Lipschitz stability of the Cauchy and Jensen equations

DOI10.1007/BF03322533zbMath0890.39023WikidataQ112226125 ScholiaQ112226125MaRDI QIDQ1377209

Jacek Tabor

Publication date: 8 July 1998

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

semigroupnormed spaceCauchy equationLipschitz stabilityJensen equationleft invariant meandouble difference property

Mathematics Subject Classification ID

Functional equations for functions with more general domains and/or ranges (39B52) Systems of functional equations and inequalities (39B72)

Related Items (15)

Erratum to: ``Quartic functional equations in Lipschitz spaces ⋮ Cauchy Difference Operator in Some Orlicz Spaces ⋮ Unnamed Item ⋮ Behavior of bi-cubic functions in Lipschitz spaces ⋮ A new type of approximation for cubic functional equations in Lipschitz spaces ⋮ Stability of generalized multi-quadratic mappings in Lipschitz spaces ⋮ Quartic functional equations in Lipschitz spaces ⋮ On approximation of approximately generalized quadratic functional equation via Lipschitz criteria ⋮ On approximate solution of Drygas functional equation according to the Lipschitz criteria ⋮ Stability of the quadratic functional equation in Lipschitz spaces ⋮ Lipschitz stability of the k-quadratic functional equation ⋮ Stability of the Cauchy type equations in the class of differentiable functions ⋮ Almost tri-cubic functions with Lipschitz condition ⋮ Superstability of the Cauchy, Jensen and isometry equations ⋮ Approximate solution of a generalized multi-quadratic type functional equation in Lipschitz spaces

Cites Work

• Stability of the Cauchy type equations in the class of differentiable functions
• Cauchy difference operator in \({\mathcal L}^p\)
• On some generalized invariant means and their application to the stability of the Hyers-Ulam type
• Functions with measurable differences
• On the Stability of the Linear Functional Equation
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