Stability of two functional equations arising from number theory

Generalizing two functional equations introduced in Houston and Sahoo (2008), Jung and Bae (2003), which arise from number theory we prove the stability of the equations f(x(1)x(2) + y(1)y(2), x(1)y(2) - x(2)y(1)) = g(x(1), y(1))h(x(2), y(2)) for all x(1), y(1), x(2), y(2) is an element of R, where f, g, h : R-2 -> R, and g(x(1), y(1), u(1), v(1))h(x(2), y(2), u(2), v(2)) = f(x(1)x(2) + y(1)y(2) + u(1)u(2) + v(1)v(2), x(1)y(2) - y(1)x(2) + u(1)v(2) - v(1)u(2,,) x(1)u(2) - y(1)v(2) - u(1)x(2) + v(1)y(2), x(1)v(2) + y(1)u(2) - u(1)y(2) - v(1)x(2)) for all x(1,) x(2,) y(1,) y(2,) u(1,) u(2,) v(1.) v(2) is an element of R, where f, g, h : R-4 -> R. (C) 2014 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.