Quadratic Functional Equations of Pexider Type
نویسنده
چکیده
First, the quadratic functional equation of Pexider type will be solved. By applying this result, we will also solve some functional equations of Pexider type which are closely associated with the quadratic equation.
منابع مشابه
4 Orthogonal stability of the Pexiderized quadratic equation ∗
The Hyers–Ulam–Rassias stability of the conditional quadratic functional equation of Pexider type f (x+y)+f (x−y) = 2g(x)+2h(y), x ⊥ y is proved where ⊥ is the orthogonality in the sense of Rätz.
متن کاملOn the Superstability of the Pexider Type Trigonometric Functional Equation
We will investigate the superstability of the hyperbolic trigonometric functional equation from the following functional equations: fx y ± gx − y λfxgy andfx y ± gx − y λgxfy, which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively.
متن کاملA Fixed Point Approach to Stability of a Quadratic Equation
Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type f(x + y) + g(x − y) = h(x) + k(y), where f, g, h, k are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on f .
متن کاملThe Superstability of the Pexider Type Trigonometric Functional Equation
The aim of this paper is to investigate the stability problem for the Pexider type (hyperbolic) trigonometric functional equation f(x + y) + f(x + σy) = λg(x)h(y) under the conditions : |f(x + y) + f(x + σy)− λg(x)h(y)| ≤ φ(x), φ(y), and min{φ(x), φ(y)}. As a consequence, we have generalized the results of stability for the cosine(d’Alembert), sine, and the Wilson functional equations by J. Bak...
متن کاملar X iv : m at h / 04 12 47 5 v 2 [ m at h . FA ] 1 2 Fe b 20 05 On the Orthogonal Stability of the Pexiderized Quadratic Equation ∗
The Hyers–Ulam stability of the conditional quadratic functional equation of Pexider type f(x + y) + f(x − y) = 2g(x) + 2h(y), x ⊥ y is established where ⊥ is a symmetric orthogonality in the sense of Rätz and f is odd. ∗2000 Mathematics Subject Classification. Primary 39B52, secondary 39B82.
متن کامل