Pointwise conditions in discrete boundary value problems with nonlocal boundary conditions

We consider summation equations having the form y(t)=γ(t)H∑i=1nαiyξi+λ∑s=0bG(t,s)f(s,y(s+1)).By utilizing a new order cone, we are able to demonstrate the existence of at least one positive solution of the equation in the case where only pointwise conditions are imposed on the function H. This is in contrast to usual approach of employing either asymptotic or interval-type conditions on this function. Finally, we provide some applications of the abstract result to discrete boundary value problems with nonlocal boundary conditions.