Fixed points and fuzzy stability of an additive-quadratic functional equation
The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation
ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY BANACH SPACES
Let M1f(x, y) : = 3 4 f(x + y)− 1 4 f(−x− y) + 1 4 f(x− y) + 1 4 f(y − x)− f(x)− f(y), M2f(x, y) : = 2f (x + y 2 ) + f (x− y 2 ) + f (y − x 2 ) − f(x)− f(y). Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities N (M1f(x, y)− ρM2f(x, y), t) ≥ t t + φ(x, y) (0.1) and N (M2f(x, y)− ρM1f(x, y), t) ≥ t t + φ(x, y) (0.2) in fuzzy Banach spaces, where ρ is a fixed real number with ρ 6= 1.
Approximately -Jordan Homomorphisms on Banach Algebras
Let , and let be two rings. An additive map is called -Jordan homomorphism if for all . In this paper, we establish the Hyers-Ulam-Rassias stability of -Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to , (b) to each approximate -Jordan homomorphism between two commutative Banach algebras there corresponds a unique -ring homomorphism near to for all .