In this article, we consider the finite-time mixed H ∞ /passivity, finite-time stability, and finite-time boundedness for generalized neural networks with interval distributed and discrete time-varying delays. It is noted that this is the first time for studying in the combination of H ∞ , passivity, and finitetime boundedness. To obtain several sufficient criteria achieved in the form of linear matrix inequalities (LMIs), we introduce an appropriate Lyapunov-Krasovskii function (LKF) including single, double, triple, and quadruple integral terms, and estimating the bound of time derivative in LKF with the use of Jensen's integral inequality, an extended single and double Wirtinger's integral inequality, and a new triple integral inequality. These LMIs can be solved by using MATLAB's LMI toolbox. Finally, five numerical simulations are shown to illustrate the effectiveness of the obtained results. The received criteria and published literature are compared.INDEX TERMS neural networks, Lyapunov-Krasovskii function, H ∞ and passivity, time-varying delays, finite-time bounded

An element [Formula: see text] of a semigroup [Formula: see text] is a called a left (respectively right) magnifying element of [Formula: see text] if [Formula: see text] (respectively [Formula: see text]) for some proper subset [Formula: see text] of [Formula: see text]. In this paper, left magnifying elements and right magnifying elements of a partial transformation semigroup will be characterized. The results obtained generalize the results of Magill [K. D. Magill, Magnifying elements of transformation semigroups, Semigroup Forum, 48 (1994) 119–126].