Positive solution for first-order discrete periodic boundary value problem

In this work, existence criteria for a positive solution for the following first-order discrete periodic boundary value problem: Δx(k)+f(k,x(k+1))=0,k∈[0,T]x(0)=x(T+1)x(0)=x(T+1) are established by using a fixed point theorem for operators on a cone. An example is also included to illustrate the importance of the result obtained.