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Some new generalized Volterra-Fredholm type nonlinear discrete inequalities involving four iterated infinite sums are established in this paper. To illustrate the validity of the established inequalities, we present some applications for them, in which new explicit bounds for the solutions of certain infinite sum-difference equations are deduced. MSC:26D15.

Some Volterra-Fredholm type nonlinear discrete inequalities involving four iterated infinite sums