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http://dx.doi.org/10.14403/jcms.2020.33.1.147

HYPERSTABILITY OF A SUM FORM FUNCTIONAL EQUATION RELATED DISTANCE MEASURES  

Lee, Young Whan (Department of Information Security, Daejeon University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.33, no.1, 2020 , pp. 147-156 More about this Journal
Abstract
The functional equation related to a distance measure f(pr, qs) + f(ps, qr) = M(r, s)f(p, q) + M(p, q)f(r, s) can be generalized a sum form functional equation as follows $${\frac{1}{n}}{\sum\limits_{i=0}^{n-1}}f(P{\cdot}{\sigma}_i(Q))=M(Q)f(P)+M(P)f(Q)$$ where f, g is information measures, P and Q are the set of n-array discrete measure, and σi is a permutation for each i = 0, 1, ⋯, n-1. In this paper, we obtain the hyperstability of the above type functional equation.
Keywords
superstability; hyperstability; stability of functional equation;
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