Algorithm Research On Generalized Splitting Problem In Hilbert Space

The split feasibility problem SFP was first introduced in 1994 by Censor and Elfving.To solve the SFP,an algorithm called the CQ-algorithm was proposed by Byrne.Split common fixed point problem SCFP was introduced by Censor and Se-gal and proposed an algorithm for solving such the problem,which also generalizes the split feasibility problem.In 2012,A.Moudafi proposed the split equality prob-lem,which also generalizes the split feasibility problem.A.Moudafi introduced the alternating CQ-algorithms and the relaxed alternating CQ-algorithms for solv-ing split feasibility problem.Recently,Chen et al.,Eslamian and Latif,Chuang and Chang and Wang introduced and studied general split feasibility problem and general split equality problem in real Hilbert spaces.In this article we studied the split problem of Hilbert mainly from two as-pects:general split common fixed point problem,general split equality problem.Firstly,we propose a new iterative algorithm for solving general split common fixed point problem,in this aspect we study a family of k-demicontractive operators.As an application,Particular cases of directed operator and quasi-nonexpansive op-erator are also considered.Then,we gave an example and numerical results to illustrate the efficiency of our algorithms.Secondly,we propose a new iterative algorithm for solving general split equality problem,in this aspect we study a fam-ily of directed operators.As an application,we consider some examples of general split equality problems and fixed point problem.Then,we give several numerical results of general split common fixed point problems to demonstrate the efficiency of the proposed algorithm.