Orthogonal stability of the generalized quadratic functional equations in the sense of Rätz

[摘要] Let ( X , ⊥) be an orthogonality module in the sense of Rätz over a unital Banach algebra A and Y be a real Banach module over A . In this paper, we apply the alternative fixed point theorem for proving the Hyers-Ulam stability of the orthogonally generalized k -quadratic functional equation of the form af(kx+y)+af(kx-y)=f(ax+ay)+f(ax-ay)+(2k2-2)f(ax)af(kx + y) + af(kx - y) = f(ax + ay) + f(ax - ay) + \left( {2{k^2} - 2} \right)f(ax) for some |k| > 1, for all a ɛ A 1 := { u ɛ A||u|| = 1} and for all x , y ɛ X with x ⊥ y , where f maps from X to Y .

[学科分类] 外科医学

[关键词] fixed point method;orthogonally generalized quadratic functional equation;stability