In the setting of a real Hilbert space H, we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations ü(t) + γu̇(t) +∇φ(u(t)) +A(u(t)) = 0, where ∇φ is the gradient operator of a convex differentiable potential function φ : H → IR, A : H → H is a maximal monotone operator which is assumed to be λ-cocoercive, and γ > 0 is a damping param...

in this article, we investigate sufficient conditions for existence of maximal and minimalsolutions to a coupled system of highly nonlinear differential equations of fractional order with mixedtype boundary conditions. to achieve this goal, we apply monotone iterative technique togetherwith the method of upper and lower solutions. also an error estimation is given to check theaccuracy of the me...

We study various error measures for approximate solution of proximal point regularizations of the variational inequality problem, and of the closely related problem of finding a zero of a maximal monotone operator. A new merit function is proposed for proximal point subproblems associated with the latter. This merit function is based on Burachik-Iusem-Svaiter’s concept of ε-enlargement of a max...

It is shown that the behavior of an m-port circuit maximal monotone elements can be expressed as a zero sum operator containing elements, and structured skew-symmetric linear representing interconnection structure, together with output transformation. The Condat–Vũ algorithm solves inclusion problems this form, may used to solve for periodic steady-state behavior, given excitation at each port,...

A new class of nonlinear set-valued variationalinclusions involving $(A,eta)$-monotone mappings in a Banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(A,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.

where T is a maximal monotone multi-valued operator and the operator C satisfies condition (S+) or (S̃+). In a regularization method by the duality operator, we use the degree theories of Kartsatos and Skrypnik upon conditions of C as well as Browder’s degree. There are two cases to consider: One is that C is demicontinuous and bounded with condition (S+); and the other is that C is quasibounded...

We introduce a new iterative algorithm for finding a common element of the solution set of the variational inequality problem for a continuous monotone mapping, the zero point set of a maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the sequence generated by the proposed algorithm to a commo...

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, convergence of the iterates, as well as pointwise and ergodic conver...