An Improved Alternating CQ Algorithm for Solving Split Equality Problems

The CQ algorithm is widely used in the scientific field and has a significant impact on phase retrieval, medical image reconstruction, signal processing, etc. Moudafi proposed an alternating CQ algorithm to solve the split equality problem, but he only obtained the result of weak convergence. The work of this paper is to improve his algorithm so that the generated iterative sequence can converge strongly.

Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem

In this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projection and obtain the weak and the strong convergence of the algorithms, respectively. Furthermore, based on the operators being quasinonexpansive, we offer an iterative algorithm to solve the extended split equality fixed point problem. We introduce a way of selecting the stepsize which does not need any prior information about operator norms in the three algorithms. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.

A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem

In this article, we introduce a relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem. Firstly, we transfer the original problem to the constrained multiple-sets split equality problem and a fixed point equation system is established. Then, we show the equivalence of the constrained multiple-sets split equality problem and the fixed point equation system. Secondly, we present a relaxed self-adaptive projection algorithm for the fixed point equation system. The advantage of the self-adaptive step size is that it could be obtained directly from the iterative procedure. Furthermore, we prove the convergence of the proposed algorithm. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

Split equality fixed point problems for asymptotically quasi-pseudocontractive operators

In this paper, we consider a split equality fixed point problem for asymptotically quasi-pseudo contractive operators which includes split feasibility problem, split equality problem, split fixed point problem etc, as special cases. Furthermore we propose a new algorithm for solving the split equality fixed point problem, and prove a weak and strong convergence theorem. The results obtained in this paper generalize and improve the recent ones announced by many others.