and Applied Analysis 3 Since weak convergence is not good for an effective algorithm, our purpose in this paper is to modify algorithm 1.3 in such a way that strong convergence is guaranteed. More precisely, for any two maximal monotone operators A and B, we define an iterative process in the following way: For x0, u ∈ H given, a sequence xn is generated using the rule x2n 1 αnu δnx2n γnJ βnx2n...

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 ...

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...

Let X be a real reflexive Banach space and A: X — 2A a maximal monotone mapping such that the graph G(A) of A is weaklyclosed in X X X and 0 £/4(0). Also, let T: X — 2A be a quasi-bounded coercive mapping of type (M) such that the effective domain D(T) of T contains a dense linear subspace X of X. Then it is shown that for each * f I co e X there exists a u e X such that co e Au + Tu and the su...

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...

We consider a nonhomogeneous first-order evolution equation governed by maximal monotone operator $ A in Hilbert space the presence of Tikhonov regularization term. study existence and strong convergence weak solutions to such systems. With boundedness conditions on central path or solution trajectory, without assuming zero set be nonempty with suitable assumptions coefficient, we prove that sy...

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...