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http://dx.doi.org/10.11568/kjm.2016.24.2.297

A FIXED POINT APPROACH TO THE STABILITY OF THE FUNCTIONAL EQUATION RELATED TO DISTANCE MEASURES  

Shiny, Hwan-Yong (Department of Mathematics Chungnam National University)
Kim, Gwang Hui (Department of Mathematics Kangnam University)
Publication Information
Korean Journal of Mathematics / v.24, no.2, 2016 , pp. 297-305 More about this Journal
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 $G^2$.
Keywords
distance measure; superstability; stability of functional equation; fixed point theorem;
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