On pexiderized Jensen-Hosszú functional equation on the unit interval

We solve the functional equation of the form 2f(x+y2)=g(x+y−xy)+h(xy) in the class of real functions defined on the unit interval [0,1]. We prove that it is not stable, but if two functions from the triple {f,g,h}  coincides the analogue equation is stable in the Hyers-Ulam sense.