The cubic ρ-functional equation in matrix non-Аrchimedean random normed spaces


Zhihua Wang, Chaozhu Hu




Using the direct method and fixed point method, we investigate the Hyers-Ulam stability of the following cubic ρ-functional equation f (x + 2y) + f (x − 2y) − 2 f (x + y) − 2 f (x − y) − 12 f (x) = ρ ( 4 f (x + y 2 ) + 4 f (x − y 2 ) − f (x + y) − f (x − y) − 6 f (x) ) in matrix non-Archimedean random normed spaces, where ρ is a fixed real number with ρ , 2.