Using the new analysis techniques, the existence and iterative approximation problem of a solution for a class of nonlinear variational inclusions with accretive type mappings are discussed in arbitrary Banach spaces. The results extend and improve some recent results.

We consider a mean value iteration for a family of functions, which corresponds to the Mann iteration with lim n→∞ α n = 0. We prove convergence results for this iteration when applied to strongly pseudocontractive or strongly accretive maps.

A class of existence theorems in the context of solving a general class of nonlinear implicit inclusion problems are examined based on A-maximal relaxed accretive mappings in a real Banach space setting.

In this paper, we continue to study convergence problems for a Ishikawa-like iterative process for a finite family of m-accretive mappings. Strong convergence theorems are established in uniformly smooth Banach spaces.

One proves the $H$-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck equation $$ u_t-\Delta\beta(u)+{\rm div}(D(x)b(u)u)=0, t\geq0, x\in\mathbb{R}^d,\qquad (1)$$ and under appropriate hypotheses on $\beta,$ $D$ $b$ convergence in $L^1_\textrm{loc}(\mathbb{R}^d)$, $L^1(\mathbb{R}^d)$, respectively, some $t_n\to\infty$ of solution $u(t_n)$ an equilibrium state large set nonn...

The purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities V ID(C, I−f) involving nonexpansive type mappings in smooth Banach spaces. We study existence of solutions of variational inequalities V ID(C, I− f) when D is the set of solutions of zeros of accretive operators or the set of fixed points of non...

During a discussion taking place at WMC’01, G. Paun put the question of what could be computed only by moving symbols between membranes. In this paper we provide some elements of the answer, in a setting similar to tissue P systems, where the set of membranes is organized into a finite graph or into a Cayley graph, and using a very simple propagation process characterizing accretive growth. Our...