About some new integral inequalities of wendroff type for discontinuous functions (Q876923)

In this paper, in a similar way to what the first author did in [Proc. X Int. Kravechuk Conf. Kyiv, 323 (2004)] for the one-dimensional case, the authors investigate the integral inequalities for discontinuous functions of two independent variables (Wendroff type) with discontinuities of non-Lipschitz type. In the second section, the authors obtained for discontinuous functions (two-dimensional case) analog results to those introduced by \textit{R. Bellman} [Duke Math. J. 10, 643--647 (1943; Zbl 0061.18502)] and \textit{I. Bihari} [Acta Math. Acad. Sci. Hung. 7, 81--94 (1956; Zbl 0070.08201)]. In the third section the authors generalized the results of the second section for integro-sum functional inequalities with delay. Finally, let us point out that many results from various authors follow directly, as special cases, from the theorems presented in this article.