Fixed Point Technique: Hyers-Ulam Stability Results Deriving From Cubic Mapping in Fuzzy Normed Spaces - Vijaya, N.; Suganthi, P.; Bagyam, Ebenesar Anna; Balamurugan, Manivannan; Prabaharan, N.; Tamilvanan, K. (Communications in Mathematics and Applications, 2024)
In this work, we introduce a novel finite-dimensional cubic functional equation align* φ(_a=1^la n_a)&=_1 ≤ a < b < c ≤ lφ(a n_a+b n_b+c n_c) &+(3-l)_1 ≤ a < b ≤ lφ(a n_a+b n_b) &+((l^2-5l+6)2)_a=0^l-1(a+1)^3φ(n_a+1), align* where l ≥ 4 is an integer, and derive its general solution. The main purpose of this work is to examine the Hyers-Ulam stability of this functional equation in fuzzy normed spaces by means of direct approach and fixed point approach.