Email this article On some equations stemming from quadrature rules
Abstract
We deal with functional equations of the type
F(y)-F(x) =(y-x)∑k=1nfk((1-λk)x+λky),
connected to quadrature rules and, in particular, we find the solutions of the following functional equation
f(x)-f(y)=(x-y)[g(x)+h(x+2y)+h(2x+y)+g(y)].
We also present a solution of the Stamate type equation
yf(x)-xf(y)=(x-y)[g(x)+h(x+2y)+h(2x+y)+g(y)].
All results are valid for functions acting on integral domains.
Keywords
Mathematics Subject Classification
References
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