Fixed Point Problems In Hilbert Spaces Research Articles

Solving equilibrium and fixed-point problems in Hilbert Spaces: A class of strongly convergent Mann-Type dual-inertial subgradient extragradient methods

Solving equilibrium and fixed-point problems in Hilbert Spaces: A class of strongly convergent Mann-Type dual-inertial subgradient extragradient methods

Iterative Solutions for Solving Variational Inequalities and Fixed-Point Problems

In this paper, we are interested in variational inequalities and fixed-point problems in Hilbert spaces. We present an iterative algorithm for finding a solution of the studied variational inequalities and fixed-point problems. We show the strong convergence of the suggested algorithm.

Weak convergence of a primal-dual algorithm for split common fixed-point problems in Hilbert spaces

Weak convergence of a primal-dual algorithm for split common fixed-point problems in Hilbert spaces

Viscosity approximation methods for solving fixed-point problems and split common fixed-point problems

In this paper, we introduce the strong convergence theorem for the viscosity approximation methods for solving the split common fixed-point problem in Hilbert spaces. As a consequence, we obtain strong convergence theorems for split variational inequality problems for Lipschitz continuous and monotone operators and split common null point problems for maximal monotone operators. Our results improve and extend the corresponding results announced by many others.

Shrinking Projection Methods for Split Common Fixed-Point Problems in Hilbert Spaces

Inspired by Moudafi (2011) and Takahashi et al. (2008), we present the shrinking projection method for the split common fixed-point problem in Hilbert spaces, and we obtain the strong convergence theorem. As a special case, the split feasibility problem is also considered.

The strong convergence of a three-step algorithm for the split feasibility problem

Based on the very recent work by Dang and Gao (Invers Probl 27:1–9, 2011) and Wang and Xu (J Inequal Appl, doi:10.1155/2010/102085, 2010), and inspired by Yao (Appl Math Comput 186:1551–1558, 2007), Noor (J Math Anal Appl 251:217–229, 2000), and Xu (Invers Probl 22:2021–2034, 2006), we suggest a three-step KM-CQ-like method for solving the split common fixed-point problems in Hilbert spaces. Our results improve and develop previously discussed feasibility problem and related algorithms.