On pexiderized Jensen–Hosszú functional equation on the unit interval

We solve the functional equation of the form 2 f ( x + y 2 ) = g ( x + y − x y ) + h ( x y ) 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.