### QUADRATIC ρ-FUNCTIONAL EQUATIONS IN β-HOMOGENEOUS NORMED SPACES

#### Abstract

In this paper, we solve the quadratic ρ-functional equations:

f(x+y)+f(x−y)−2f(x)−2f(y)

= ρ(4f ( x + y / 2) + f (x − y) − 2f (x) − 2f (y) )----(1)

and

4f (x + y / 2) + f (x − y) − 2f (x) − 2f (y)

= ρ(f(x+y)+f(x−y)−2f(x)−2f(y)),------(2)

where ρ is a fixed complex number with ρ≠1.

Using the direct method, we prove the Hyers-Ulam stability of the quadratic ρ-functional equations (1) and (2) in β-homogeneous complex Banach spaces.

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**ISSN: 1229-1595 (Print), 2466-0973 (Online)**