On Stability of a General n-Linear Functional Equation
نویسندگان
چکیده
Let X be a linear space over K∈{R,C}, Y real or complex Banach and f:Xn→Y. With some fixed aji,Ci1…in∈K (j∈{1,…,n}, i,ik∈{1,2}, k∈{1,…,n}), we study, using the direct point methods, stability general of equation f(a11x11+a12x12,…,an1xn1+an2xn2)=∑1≤i1,…,in≤2Ci1…inf(x1i1,…,xnin), for all xjij∈X (j∈{1,…,n},ij∈{1,2}). Our paper generalizes several known results, among others concerning equations with symmetric coefficients, such as multi-Cauchy multi-Jensen well multi-Cauchy–Jensen equation. We also prove hyperstability above in m-normed spaces m≥2.
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ژورنال
عنوان ژورنال: Symmetry
سال: 2022
ISSN: ['0865-4824', '2226-1877']
DOI: https://doi.org/10.3390/sym15010019