Motivated by [Science in China (Ser. A Mathematics) 36 (2006), no. 7, 721?732], this article deals with the following discrete type BVP $LARGEleft{{{;{Delta}[{phi}({Delta}x(n))];+;f(n,;x(n;+;1),{Delta}x(n),{Delta}x(n + 1));=;0,;n;{in};[0,N],}}\{;{x(0)-{sum}^m_{i=1}{alpha}_ix(n_i) = A,}}\{;{x(N+2)-;{sum}^m_{i=1}{eta}_ix(n_i);=;B.}} ight.$ The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operator ${Delta}$x(n).