We study the convergence of a Douglas-Rachford type splitting algorithm for the infinite dimensional stochastic differential equation dX + A(t)(X)dt = X dW in (0, T ); X(0) = x, where A(t) : V → V ′ is a nonlinear, monotone, coercive and demicontinuous operator with sublinear growth and V is a real Hilbert space with the dual V ′. V is densely and continuously embedded in the Hilbert space H an...

The starting point of this paper is the recent important work of F. E. Browder, who extended degree theory to operators of monotone type. The degree function of Browder is generalized to maps of the form T+f+G , where T is maximal monotone, f is of class (S)+ bounded, and G{ •) is an u.s.c. compact multifunction. It is also generalized to maps of the form f+NG , with / of class (5)+ and 7VC the...

Let C be a closed convex subset of a real Hilbert space H . Let A be an inverse-strongly monotone mapping of C into H and let B be a maximal monotone operator on H such that the domain of B is included in C . We introduce two iteration schemes of finding a point of (A+B)−10, where (A+B)−10 is the set of zero points of A+B. Then, we prove two strong convergence theorems of Halpern’s type in a Hi...

zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎a strong convergence theorem for the common solutions of the problems is established in the framework of hilbert spaces‎.

Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].

We provide and analyze a based average for two convex functions, based on a kernel function. It covers several known averages such as the arithmetic average, epigraphical average, and the proximal average. When applied to the Fitzpatrick function and the conjugate of Fitzpatrick function associated with a monotone operator, our average produces an autoconjugate (also known as selfdual Lagrangia...

In this paper, we address the problem of boundary stabilization heat equation subjected to an unknown disturbance, which is assumed be acting at flux condition. By means Lyapunov techniques and use sign multivalued operator, responsible rejecting effects design a feedback law obtain exponential stability closed-loop system. The well-posedness system, differential inclusion, shown with maximal m...