Hyers–Ulam–Rassias Stability of a Jensen Type Functional Equation

On a Jensen Type Functional Equation

“…We are going to examine functional equation (1) where a, b are nonnegative constants and f is an unknown function defined in M with values in S. Equation (1) in the case a = 3, b = 2 was studied in the paper of Tiberiu Trif [8] in the class of functions f : X → Y , where X and Y are real vector spaces. For the same a and b equation (1) was considered in [6] for functions f : M → S. In paper [6] it has been shown that every solution of the equation…”

Popoviciu Type Equations on Cylinders

“…Then, according to Theorem 2.1, there exist functions a, f : G → H and a b ∈ H such that f satisfies (7), (8)- (11) hold and F is of the form (12). Applying Corollary 3.2, we get (21). Moreover (cf.…”

“…This result has been generalized by Trif [21], who has proved that if X and Y are real linear spaces, then a function f : X → Y satisfies Eq. for x ∈ X.…”

On the stability of the linear functional equation in a single variable on complete metric groups

“…A generalized Hyers-Ulam stability of the gamma functional equation was obtained by S.-M. Jung in [14]. A nice result on generalized Hyers-Ulam stability of the equation (1.1) was obtained by T. Trif [20] for functions f acting from an arbitrary nonempty set S into a Banach space X.…”