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Hyperstability of the Jensen functional equation. (English) Zbl 1299.39022
S.-M. Jung, M. S. Moslehian and 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 $$X$$.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B62 Functional inequalities, including subadditivity, convexity, etc. 47H14 Perturbations of nonlinear operators 47H10 Fixed-point theorems 47J20 Variational and other types of inequalities involving nonlinear operators (general)
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##### References:
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