%0 Journal Article
%T On some equations stemming from quadrature rules
%A Barbara Kocl£¿ga-Kulpa
%A Tomasz Szostok
%A Szymon W£¿sowicz
%J Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
%D 2009
%I Krak¨®w : Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
%X We deal with functional equations of the type $$F(y)-F(x) =(y-x)sum_{k=1}^nf_k((1-lambda_k)x+lambda_ky),$$ 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.
%U http://studmath.up.krakow.pl/index.php/studmath/article/view/81