In this paper, we define Ap weights, briefly discuss the theory of weighted inequalities and its application and importance in various fields. We then prove that for an Ap weight function w and for some , the function, min(w, k) is an Ap weight function. Finally we establish the weighted inequality for min(w, k).DOI: http://dx.doi.org/10.3126/jie.v10i1.10887Journal of the Institute of Engineering, Vol. 10, No. 1, 2014 pp. 121–124