Nonlinear discrete inequalities with two variables and their applications

An error in the proof of Theorem 1 by Zheng et al. [K. Zheng, Y. Wu, S. Zhong, Discrete nonlinear integral inequalities in two variables and their applications, Appl. Math. Comput. 207 (2009) 140–147] is reported. This paper gives the right proof under some additional condition. Application examples to show boundedness and uniqueness of solutions of a Volterra type difference equation are also given.