Orthogonal stability of a quadratic functional inequality: a fixed point approach

Abstract

Let f : X → Y be a mapping from an orthogonality space (X , ⊥) into a real Banach space (Y, k · k). Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally quadratic functional inequality for all x, y, z ∈ X with x⊥y, x⊥z and y⊥z