Iterative oscillation criteria for first-order difference equations with non-monotone advanced arguments

Consider the first-order linear advanced difference equation of the form del x(n) - q(n) x(sigma (n)) = 0, n is an element of N, where (q(n))(n >= 1) is a sequence of nonnegative real numbers and (sigma(n))(n >= 1) is a sequence of integers such that sigma(n) >= n + 1, for all n is an element of N. Based on an iterative procedure, new oscillation criteria, involving lim sup, are established in the case of non-monotone advanced argument. Our conditions essentially improve several known results in the literature. Examples, numerically solved in Maple software, are also given to illustrate the applicability and strength of the obtained conditions over known ones.