In this paper we consider primal and dual parametric vector Ky Fan inequality in metric linear spaces. Using the strong convexity and H¨older continuity for vector valued mappings, without strong monotonicity assumption, we establish the sufficient conditions for the solution mappings to these problems to be H¨older continuous around the reference point, when the solution of these problems is not unique. Many examples are provided to illustrate that the imposed assumptions are essential and our results are different from the existed ones in the literature.