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HYPERSTABILITY OF A SUM FORM FUNCTIONAL EQUATION RELATED DISTANCE MEASURES

  • Received : 2019.11.18
  • Accepted : 2020.01.31
  • Published : 2020.02.15

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

Acknowledgement

This research was supported by the Daejeon University Research Grants (2019).

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