Some existence results on best approximation are proved without starshaped subset and affine mapping in the set up of q-normed space. First, we consider the closed subset and then weakly compact subsets for said purpose. Our results improve the result of Mukherjee and Som [11] and Jungck and Sessa [7] and some known results [4], [9], [12] are obtained as consequence. To achieve our goal, we have introduced a property known as "Property(A)".