Superstability and stability of \((r,s,t)\)-\(J^*\)-homomorphisms: fixed point and direct methods (Q2794905)
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scientific article; zbMATH DE number 6554582
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Superstability and stability of \((r,s,t)\)-\(J^*\)-homomorphisms: fixed point and direct methods |
scientific article; zbMATH DE number 6554582 |
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11 March 2016
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functional equation
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Hyers-Ulam stability
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fixed point method
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\((r,s,t)\)-\(J^*\)-homomorphism
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Superstability and stability of \((r,s,t)\)-\(J^*\)-homomorphisms: fixed point and direct methods (English)
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The authors prove superstability and Hyers-Ulam stability of \((r,s,t)\)-\(J^*\)-homomorphisms associated to the functional equations \(f(x+y)+f(x-2y)+f(y-x)=f(x)\) and NEWLINE\[NEWLINEf\left(\frac{\sum_{i=1}^px_i}{p-1}\right)+\sum_{i=2}^pf\left(\frac{\sum_{j=1, j\neq i}^px_j-px_i}{p-1}\right)+f\left(\frac{\sum_{i=2}^px_i-x_1}{p-1}\right)=f(x_1).NEWLINE\]NEWLINE The paper is related to [\textit{C. Baak} and \textit{M. S. Moslehian}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 63, No. 1, 42--48 (2005; Zbl 1085.39026)] being missed from the long list of references.
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0.8568506836891174
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0.8253539800643921
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0.8249602317810059
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