Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A FIXED POINT APPROACH TO THE STABILITY OF THE FUNCTIONAL EQUATION RELATED TO DISTANCE MEASURES

  • Received : 2016.02.11
  • Accepted : 2016.05.17
  • Published : 2016.06.30
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Abstract

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

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References

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