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...

In this paper, we introduce the iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space and then obtain the sequence converges strongly to a common element of two sets. The results extended and improved the corresponding results of Plubtieng and Punpaeng [S. Plubtieng, R. ...

In this paper, we introduce two modified hybrid iterative methods (one implicit method and one explicit method) for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality problem for a continuous monotone mapping and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces, and show...

In this paper, we pursue two purposes. Our first goal is to study a new system of extended multi-valued nonlinear variational inclusions in Banach spaces and establish its equivalence with fixed point problems the help concept (H, ?)-proximal mapping. The obtained alternative equivalent formulation used iterative algorithm for finding approximate solution proposed. Under some appropriate assump...

Let {Ti}i=1 be a finite family of nonexpansive self-maps of H . Denote the common fixed points set of {Ti}i=1 by ⋂N i=1 Fix(Ti). Let F : H → H be a mapping such that for some constants k,η > 0, F is k-Lipschitzian and η-strongly monotone. Let {αn}n=1 ⊂ (0,1), {λn}n=1 ⊂ [0,1) and take a fixed number μ ∈ (0,2η/k2). The iterative schemes concerning nonlinear operators have been studied extensively...

We show that a compactum is locally connected if and only if every semimonotone mapping onto it is also monotone. If we put open in place of monotone, we obtain the finite compacta; if we put in confluent, we obtain a large class of compacta, the connected members of which are connected im kleinen at each of their cut points.