in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the p...

Inspired by the very recent work by Noor and Noor [9] and given a closed convex set-valued mapping C, we propose a split algorithm for solving the problem of finding an element x∗ which is a zero of a given maximal monotone operator T such that its image, Ax∗, under a linear operator, A, is in a closed convex set C(x∗). Then, we present two strong convergence results and state some examples as ...

A numerical method is developed for fire spread simulation modelling. The two dimensional surface model presented takes into account moisture content, radiation, wind and slope effects, which are by far the most important mechanisms in fire spread. We consider the combustion of a porous solid, where the energy conservation equation is applied. The influence of moisture content and eventually he...

In this paper, we introduce and analyze some generalized hybrid proximal point algorithms for finding a common element of the set of zeros of a maximal monotone operator and the set of fixed points of a nonexpansive mapping in a Hilbert space. These algorithms include the previously known proximal point algorithms as special cases. Weak and strong convergence of the proposed proximal point algo...

Consider a bounded domain G C R (_N>1) with smooth boundary T . Let L be a uniformly elliptic linear differential operator. Let y and ß be two maximal monotone mappings in R. We prove that, when y ? 2 satisfies a certain growth condition, given f £ L (G ) there is u € H (G) such that Lu + y(u) 3 f a.e. on G, and -du/d v e ß(u\ ) a.e. on T, where du/civ is the conormal derivative associated with...

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximalprojection method is, essentially, a fixed point procedure and our convergence results are based on new generalizations of Lemma Opial. We show how the proximal-projection meth...

is called the effective domain of F, and F is said to be locally bounded at a point x e D(T) if there exists a neighborhood U of x such that the set (1.4) T(U) = (J{T(u)\ueU} is a bounded subset of X. It is apparent that, given any two monotone operators Tx and T2 from X to X*, the operator F», + T2 is again monotone, where (1 5) (Ti + T2)(x) = Tx(x) + T2(x) = {*? +x% I xf e Tx(x), xt e T2(x)}....

By embedding the notion of splitting within a general separator projection algorithmic framework, we develop a new class of splitting algorithms for the sum of two general maximal monotone operators in Hilbert space. Our algorithms are essentially standard projection methods, using splitting decomposition to construct separators. These projective algorithms converge under more general condition...