This paper deals with global convergence to equilibria, and in particular Hirsch’s generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems.

Let $E$ be a uniformly smooth and convex real Banach space $E^*$ its dual space. Suppose $A : E\rightarrow E^*$ is bounded, strongly monotone satisfies the range condition such that $A^{-1}(0)\neq \emptyset$. Inspired by Alber [2], we introduce Lyapunov functions use new geometric properties of spaces to show strong convergence an iterative algorithm solution $Ax=0$.

For $C^{1}$-smooth strongly monotone discrete-time dynamical systems, it is shown that “convergence to linearly stable cycles” a prevalent asymptotic behavior in the measure-theoretic sense. The results are then applied several classes of time-periodic parabolic equations and obtain prevalence convergence periodic solutions.

We prove necessary and sufficient conditions for locally Lipschitz Löwner operators to be monotone, strictly monotone and strongly monotone. Utilizing our characterization of the strict monotonicity of Löwner operators, we generalize Mangasarian class of Nonlinear Complementarity Problem (NCP)-functions to the setting of symmetric cone complementarity problem. This affirmatively answers a quest...

Approximation-solvability of a class of nonlinear implicit variational inequalities involving a class of partially relaxed monotone mappings a computation-oriented class in a Hilbert space settingis presented with some applications. Partially Strongly Monotone Mapping, Partially Relaxed Mono