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General solution and stability of Quattuorvigintic functional equation in matrix paranormed spaces. (English) Zbl 1434.39022

The authors consider the following functional equation: \begin{multline*} Df(v,w) = f(v+12w)-24f(v+11w)+276f(v+10w)-2024f(v+9w)\\ + 10626f(v+8w)-42504f(v+7w)+134596f(v+6w)-346104f(v+5w)\\ + 735471f(v+4w)-1307504f(v+3w)+1961256f(v+2w)-2496144f(v+w)\\ + 2704156f(v)-2496144f(v-w)+1961256f(v-2w)-1307504f(v-3w)\\ + 735471f(v-4w)+134596f(v-6w)-42504f(v-7w)+10626f(v-8w)\\ - 2024f(v-9w)+276f(v-10w)-346104f(v-5w)-24f(v-11w)\\ + f(v-12w) -1.124000728-10^{21}f(w), \end{multline*} which is called quattuorvigintic functional equation since the function \(f(x)=cx^{24}\) is its solution. They provide the general solution of this functional equation and prove its Hyers-Ulam stability in matrix paranormed spaces by using a fixed point approach and a direct method. The motivation behind the above functional equation is not clear from the text.

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
39B82 Stability, separation, extension, and related topics for functional equations
47H10 Fixed-point theorems
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References:

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