In this paper, we use the Yoshida approximation to prove the existence and uniqueness of a solution for the backward doubly stochastic differential equation when the generator is monotone and continuous. Before that we present the results for existence and uniqueness of an adapted solution of the backward doubly stochastic differential equation under some generals conditions.

We develop a generalized approximation method (GAM) to obtain solution of a steady state one-dimensional nonlinear convective-radiative-conduction equation. The GAM generates a bounded monotone sequence of solutions of linear problems. The sequence of approximants converges monotonically and rapidly to a solution of the original problem. We present some numerical simulation to illustrate and co...

For a maximal monotone operator T in a Banach space an iterative solution of 0 ∈ Tx has been found through weak and strong convergence of resolvents of these operators. Identity mapping in the definition of resolvents has been replaced by the duality mapping. Solution after finite steps has also been established.

— Tofind a zero of the sum of two maximal monotone operators, we analyze a twosteps algorithm where the problem is first approximated by a regularized one and the regularization parameter is then reduced to converge to a solution of the original problem. We give a formai proof of the convergence which, in that case, is not ergodic. The main resuit is a generalization of one given by Brezis [4] ...

We introduce the new iterative methods for finding a common solution set of monotone, Lipschitztype continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space. The main result extends various results existing in the current...

In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the uniform convergence of the solution of the oscillating systems to the bounded uniformly continuous solution of the homogenized system.

Most asymptotic convergence analysis of interior-point algorithms for monotone linear complementarity problems assumes that the problem is nondegenerate, that is, the solution set contains a strictly complementary solution. We investigate the behavior of these algorithms when this assumption is removed.

In this study, we examine the monotone convergence of Newton-like methods to a solution of an equation on a partially ordered topological space setting. In particular we provide suucient conditions for the construction of accelerating sequences. This way the solution is obtained faster than in earlier results.

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

We develop a monotone approximation to the solution of an age-structured model which describes the regulation of erythropoiesis, the process by which red blood cells are developed. The convergence of this approximation to the unique solution of the model is also established.