M. Arunkumar

Various generalized Ulam-Hyers stabilities of a nonic functional equations

Abstract In this paper, we have established the general solution and generalized Ulam - Hyers stability of the following nonic functional equation f(x + 5y) - 9f(x + 4y) + 36f(x + 3y) - 84f(x + 2y) + 126f(x + y) - 126f(x) + 84f(x - y) - 36f(x - 2y) + 9f(x - 3y) - f(x - 4y) = 9!f(y) where 9! = 362880 in a Banach Space (BS), Felbins type Fuzzy Normed Space (FFNS) and Intuitionistic Fuzzy Normed Space (IFNS) using the standard direct and fixed point method.

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

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.