Approximation of the multi-\(m\)-Jensen-quadratic mappings and a fixed point approach. (English) Zbl 1479.39026
Summary: In this article, by using a new form of multi-quadratic mapping, we define multi-\(m\)-Jensen-quadratic mappings and then unify the system of functional equations defining a multi-\(m\)-Jensen-quadratic mapping to a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability of multi-quadratic and multi-\(m\)-Jensen-quadratic functional equations. As a consequence, we show that every multi-\(m\)-Jensen-quadratic functional equation (under some conditions) can be hyperstable.
MSC:
| 39B12 | Iteration theory, iterative and composite equations |
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 46B03 | Isomorphic theory (including renorming) of Banach spaces |
| 47H10 | Fixed-point theorems |
Keywords:
Banach space; multi-Jensen mapping; multi-quadratic mapping; multi-\(m\)-Jensen mapping; Hyers-Ulam stability; fixed pointReferences:
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