Stability of cubic and quartic rho-functional inequalities in fuzzy normed spaces

In this paper, we solve the following cubic ρ-functional inequality N(f(2x+y)+f(2x−y)−2f(x+y)−2f(x−y)−12f(x)−ρ(4f(x+y/2)+4f(x−y/2)−f(x+y)−f(x−y)−6f(x));t)≥t/t+φ(x;y)(1) and the following quartic ρ-functional inequality N(f(2x+y)+f(2x−y)−4f(x+y)−4f(x−y)−24f(x)+6f(y)−ρ(8f(x+y/2)+8f(x−y/2)−2f(x+y)−2f(x−y)−12f(x)+3f(y));t)≥t/t+φ(x;y)(2) in fuzzy normed spaces, where ρ is a fixed real number with ρ ≠ 2 . Using the direct method, we prove the Hyers-Ulam stability of the cubic ρ -functional inequality (1) and the quartic ρ -functional inequality (2) in fuzzy Banach spaces.