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In this paper, the authors introduce and establish the general solution and generalized UlamHyers stability of a ri type n− dimensional Quadratic-Cubic functional equation n ∑ i=0 [ f (r2ix2i + r2i+1x2i+1)] = n ∑ i=0 ( 1 ∑ u=0 [ 1 ∑ v=0 ( r2ir2i+1(−1) + r2ir 2i+1(−1) + r2 2ir2i+1(−1) 4 ) ( f ((−1)x2i +(−1)x2i+1)) ] + ( r3 2i + r 2 2i− r2ir 2i+1 4 ) f (x2i)+ ( r2 2i− r3 2i + r2ir 2i+1 4 ) f (−x2i) + ( r3 2i+1 + r 2 2i+1− r2 2ir2i+1 4 ) f (x2i+1)+ ( r2 2i+1− r3 2i+1 + r2 2ir2i+1 4 ) f (−x2i+1) ) where r2i,r2i+1 ∈ R−{0}, (i = 0,1,2 · · ·n) and n is a positive integer in Random normed spaces.

malaya journal of matematik

General solution and generalized Ulam - Hyers stability of ri􀀀 type n dimensional quadratic-cubic functional equation in random normed spaces: Direct and fixed point methods