Extra-gradient methods for solving split feasibility and fixed point problems

Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems

and Applied Analysis 3 in medical image reconstruction. A number of image reconstruction problems can be formulated as the SFP; see, for example, 11 and the references therein. Recently, it is found that the SFP can also be applied to study intensity-modulated radiation therapy IMRT 12–14 . In the recent past, a wide variety of iterative methods have been used in signal processing and image rec...

The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems

and Applied Analysis 3 open topic. For example, it is yet not clear whether the dual approach to (7) of [29] can be extended to the SFP. The original algorithm given in [15] involves the computation of the inverse A (assuming the existence of the inverse of A), and thus has not become popular. A seemingly more popular algorithm that solves the SFP is the CQ algorithm of Byrne [16, 21] which is ...

Shrinking projection methods for solving split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings in Hilbert spaces

In this paper, we propose a new iterative sequence for solving common problems which consist of split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings in the framework of Hilbert spaces and prove some strong convergence theorems of the generated sequence {xn} by the shrinking projection method. Our results improve and extend the previous results given in th...

The Hybrid Extragradient Method for the Split Feasibility and Fixed Point Problems

In this paper, we suggest a hybrid extragradient method for finding a common element of the set of fixed point sets of an infinite family of nonexpansive mappings and the solution set of the split feasibility problem (SFP) in real Hilbert spaces.

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems