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On Hyers–Ulam stability of generalized linear functional equation and its induced Hyers–Ulam programming problem

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Abstract

We propose a new approach called Hyers–Ulam programming to discriminate whether a generalized linear functional equation, with the form \({\sum_{i=1}^m L_if(\sum_{j=1}^n a_{ij}x_j) = 0}\) for functions from a normed space into a Banach space, has the Hyers–Ulam stability or not. Our main result is that if the induced Hyers–Ulam programming has a solution, then the corresponding functional equation possesses the Hyers–Ulam stability.

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Zhang, D. On Hyers–Ulam stability of generalized linear functional equation and its induced Hyers–Ulam programming problem. Aequat. Math. 90, 559–568 (2016). https://doi.org/10.1007/s00010-015-0393-8

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  • DOI: https://doi.org/10.1007/s00010-015-0393-8

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