The paper is concerned with discrete equations of Volterra type
x(n)=fn(n,x(n),x(n1),x(n0+1),x(n0)),n=n0,n0+1,
where Δ is the forward difference,x(n)=x(n+1)x(n+1)x(n),fn:nn0+2,n0,n,nn0. A problem on the existence of solutions x: {n0, n0 + 1,...}→ ℝ, such that their graph lies in a given domain is solved. Sufficient conditions guaranteeing such a property of solutions are given. A relation with fractional discrete equations is discussed.
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