Random fixed point results in the framework of a compact and weakly compact domain of a q-normed spaces which is not necessary star-shaped have been obtained in the present work. Invariant random approximation results have also been determined as an application. In this way, a random version of invariant approximation results due to R.N. Mukherjee and T. Som (A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16 (3), 243-244, 1985) and S.P. Singh.