Hyperstability of the Jensen functional equation
Copyright policy )Hyperstability of the Jensen functional equation
\textit{S.-M. Jung}, \textit{M. S. Moslehian} and \textit{P. K. Sahoo} [J. Math. Inequal. 4, No. 2, 191--206 (2010; Zbl 1219.39016)] investigated the conditional stability of the generalized Jensen functional equation \(f(ax+by)=af(x)+bf(y)\). Based on a fixed point method, the authors of the present paper consider the hyperstability problem of the classical Jensen equation \(f\left(\frac{x+y}{2}\right)=\frac{f(x)+f(y)}{2}\), where \(f\) is a mapping from a normed space \(X\) into a Banach space \(Y\) such that \(x, y, (x+y)/2\) are in a nonempty subset \(U\) of \(X\).
- Pedagogical University Mozambique
conditional stability, Fixed-point theorems, Jensen equation, Variational and other types of inequalities involving nonlinear operators (general), Stability, separation, extension, and related topics for functional equations, fixed point theorem, Functional inequalities, including subadditivity, convexity, etc., Perturbations of nonlinear operators, hyperstability
conditional stability, Fixed-point theorems, Jensen equation, Variational and other types of inequalities involving nonlinear operators (general), Stability, separation, extension, and related topics for functional equations, fixed point theorem, Functional inequalities, including subadditivity, convexity, etc., Perturbations of nonlinear operators, hyperstability
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