Stability of an additive-quadratic functional equation in modular spaces

Abstract

Using the direct method, we prove the Hyers-Ulam-Rassias stability of the following functional equation: ϕ(x+y,z+w)+ϕ(x−y,z−w)−2ϕ(x,z)−2ϕ(x,w)=0\phi \left(x+y,z+w)+\phi \left(x-y,z-w)-2\phi \left(x,z)-2\phi \left(x,w)=0 in ρ\rho -complete convex modular spaces satisfying Fatou property or Δ2{\Delta }_{2}-condition.

Keywords

• hyers-ulam-rassias stability
• additive-quadratic functional equation
• modular space
• fatou property
• δ2-condition
• 39b82
• 39b52