In this paper, we introduce and study a new class of generalized nonlinear mixed quasi-variational inequalities involving maximal η-monotone mapping. Using the resolvent operator technique for maximal η-monotone mapping, we prove the existence of solution for this kind of generalized nonlinear multi-valued mixed quasi-variational inequalities without compactness and the convergence of iterative...

This paper deals with numerical solving semilinear parabolic problems based on the method of upper and lower solutions. A monotone iterative method with quadratic convergence rate is constructed. The monotone iterative method combines an explicit construction of initial upper and lower solutions and the modified accelerated monotone iterative method. The monotone iterative method leads to the e...

In this article we develop both the a priori and a posteriori error analysis of hp– version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ R, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm which are explicit in the local ...

We propose a monotone multigrid method based on a B–spline basis of arbitrary smoothness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi–optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B–spline expan...

We propose a monotone multigrid method based on a B–spline basis of arbitrary smoothness for the efficient numerical solution of elliptic variational inequalities on closed convex sets. In order to maintain monotonicity (upper bound) and quasi–optimality (lower bound) of the coarse grid corrections, we propose coarse grid approximations of the obstacle function which are based on B–spline expan...

Riemann conjectured that all the zeros of the Riemann Ξ-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ΞN (z) in Riemann’s uniformly convergent infinite series expansion of Ξ(z) involving incomplete gamma functions. We conjecture that when the zeros of ΞN (z) in the first quadrant of the complex pla...

In this Letter, by utilizing the Lyapunov functional method, applying M-matrix and topological degree theory, we analyze the global exponential stability and the existence of periodic solutions of a class of recurrent neural networks with delays. Some simple and new sufficient conditions ensuring existence, uniqueness and global exponential stability of the equilibrium point and periodic soluti...

This note presents new results on global asymptotic stability (GAS) and global exponential stability (GES) of a general class of continuous-time recurrent neural networks with Lipschitz continuous and monotone nondecreasing activation functions. We first give three sufficient conditions for the GAS of neural networks. These testable sufficient conditions differ from and improve upon existing on...

In this paper, we study the complete convergence and complete moment convergence for weighted sums of extended negatively dependent (END) random variables under sub-linear expectations space with the condition of [Formula: see text], further [Formula: see text], [Formula: see text] ([Formula: see text] is a slow varying and monotone nondecreasing function). As an application, the Baum-Katz type...