Filomat 2011 Volume 25, Issue 3, Pages: 43-54
https://doi.org/10.2298/FIL1103043G
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Stability of a mixed type additive, quadratic and cubic functional equation in random normed spaces
Gordji Eshaghi Madjid (Department of Mathematics, Semnan University, Semnan, Iran + Research Group of Nonlinear Analysis and Applications (RGNAA), Semnan, Iran + Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Iran)
Savadkouhi Bavand Meysam (Department of Mathematics, Semnan University, Semnan, Iran + Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Iran)
In this paper, we obtain the general solution and the stability result for
the following functional equation in random normed spaces (in the sense of
Sherstnev) under arbitrary t-norms f(x+3y)+f(x−3y)= 9(f(x+y)+f(x−y))−16f(x).
Keywords: Additive functional equation, Quadratic functional equation, Cubic functional equation, Random normed space