A Fixed Point Approach to Stability of a Quadratic Equation

Abstract

Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type $f(x+y)+g(x-y)=h(x)+k(y)$, where $f,g,h,k$ are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on $f$.

16 pages, to appear in Bulletin of the Brazilian Mathematical Society

References in corpus (2)

• On the Orthogonal Stability of the Pexiderized Quadratic Equation
• On the stability of the orthogonal Pexiderized Cauchy equation

Cited by in corpus (2)

• Fuzzy almost quadratic functions
• The stability of a quadratic type functional equation with the fixed point alternative