In this paper, we study the weak convergence of the algorithms for solving variational inclusion problems without using Lipschitz condition of the inverse strongly monotone operator in real Hilbert spaces. The algorithms are inspired by Tseng’s modied forward-backward splitting method [4](SIAM J Control Optim 38,431-446(2000))with a simple step size. The weak convergence theorems for our algorithms are established without any requirement of additionally resolvent operators and the prior knowledge of the bounded linear operator norm. Also, our methods are extended to solve the split feasible problem and split minimization problem. Finally, some numerical experiments are provided to demonstrate the eciency of the proposed iterative method.

Previous literature has proved that there exists a unique solution about multifactor uncertain differential equation (MUDE for short) when their coefficients satisfy strict global Lipschitz continuous condition. In this paper, firstly, we consider new existence and uniqueness theorem under the weaker local Lipschitz continuous condition. The next, when the coefficients do not satisfy the Lipschitz condition, we just showcase existence theorem under continuous and linear growth conditions. Once more, we establish the inverse uncertainty distributions (IUDs for short) of supremum, infimum and time integral about the uncertain process Zk, meanwhile, we design some numerical algorithms for solving these IUDs. In the end, some numerical examples are presented to verify the effectiveness of algorithms.