In this paper, we deal with the problem of finding a common fixed point of a family of relatively nonexpansive mappings. We, first of all, discuss the properties of strongly relatively nonexpansive mappings and show a strong convergence theorem for a sequence of relatively nonexpansive mappings under some conditions. Using this result, we obtain a strong convergence theorem for a finite family ...

Under some weaker conditions, we prove the strong convergence of the sequence generated by a modified regularization method of finding a zero for a maximal monotone operator in a Hilbert space. In addition, an example is also given in order to illustrate the effectiveness of our generalizations. The results presented in this paper can be viewed as the improvement, supplement, and extension of t...

In this paper we study a model of ferromagnetic material with hysteresis effects. The magnetic moment behaviour is described by the non-linear Landau-Lifschitz equation with an additional term modelling the hysteresis. This term takes the form of a maximal monotone operator acting on the time derivative of the magnetic moment. In our model, it is approximated via a relaxing heat equation. For t...

In this paper we study existence and uniqueness of solutions for the boundary-value problem, with initial datum in L1(Ω), ut = div a(x, Du) in (0,∞)×Ω, − ∂u ∂ηa ∈ β(u) on (0,∞)× ∂Ω, u(x, 0) = u0(x) in Ω, where a is a Carathéodory function satisfying the classical Leray-Lions hypothesis, ∂/∂ηa is the Neumann boundary operator associated to a, Du the gradient of u and β is a maximal monotone grap...

Within a nonzero, real Banach space we study the problem of characterising a maximal extension of a monotone operator in terms of minimality properties of representative functions that are bounded by the Penot and Fitzpatrick functions. We single out a property of this space of representative functions that enable a very compact treatment of maximality and pre-maximality issues. This Paper is D...

The Non Smooth Dynamical Systems (NSDS) are a very special kind of dynamical systems characterized by their nonsmoothness in the evolution with respect to time and by a set of non smooth generalized equations. The so-called Moreau’s Sweeping Process[9, 10] is a special kind of differential inclusion with a maximal monotone operator[5] which appears to be a very nice formulation for the unilater...

Existence analysis of primal and dual evolution mixed variational inclusions is performed on the basis of duality principles, rendering primal and dual solvability equivalence, respectively. Via a fixed-point maximal monotone subdifferential resolvent characterization, corresponding existence results are established under a strong monotonicity condition for the time derivative-elliptic combined...

The Non Smooth Dynamical Systems (NSDS) are a very special kind of dynamical systems characterized by their nonsmoothness in the evolution with respect to time and by a set of non smooth generalized equations. The so-called Moreau’s Sweeping Process[9, 10] is a special kind of differential inclusion with a maximal monotone operator[5] which appears to be a very nice formulation for the unilater...

In this paper, we consider the stabilization problem of a one-dimensional wave equation with unknown disturbance. In order to stabilize the system with disturbance, we design a distributed feedback controller by employing the idea of sliding mode control technology. For the resulted nonlinear closed-loop system, we prove its solvability by using the maximal monotone operator. Further we prove t...

We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse stronglymonotone in a Banach space under different conditions. Moreover, applications to complementarit...