In this paper, we prove some results concerning the existence of invariant best approximation in Banach spaces. Our main result improves the corresponding results of Jungck and Hussain, Hussain et.al. In the sequel, we discuss some results on best simultaneous approximation in ordered semi-convex structure.

Let A = kG, the group algebra of some finite group where the characteristic of the field k divides |G|. In contrast to working over the complex field, the kGmodules are not usually semisimple. If a Sylow p-subgroup of G is not cyclic then there are infinitely many indecomposable kG-modules, and we usually enjoy little control over the category of such modules. It is therefore an important probl...

and Applied Analysis 3