The Convergence Throrems Of The Solution Of Split Equality Fixed Point Problems With Applications

In 2013,Moudafi proposed the split equality problem(SEP)and studied the weak convergence theorems of the split equality problem(SEP).In 2014,Moudafi proposed the split equality fixed point problem(SEFPP)and introduced a new alternating iterative algorithm to investigate SEFPP of nonexpansive mappings,the weak convergence theorems of the iterative scheme proposed are obtained.At present,the research on the split equality fixed point problem in Hilbert s-paces is very extensive,but it is still not perfect.The main research is aimed at some special and strong constraint condition mappings,such as nonexpansive mapping,firmly nonexpansive mapping,strong quasi-nonexpansive mapping and demicontractive mapping,etc.In addition,many of the strong convergence the-orems of the algorithms with the assumption of semi-compactness conditions are obtained.For the above problems,in the framework of Hilbert spaces,the strong and weak convergence theorems of the SEFPP for total asymptotically strictly pseudo-contractive mappings are obtained.Furthermore,the strong convergence theorems of an new iterative algorithm by using the hybrid projection method are also obtained without assumption of semi-compactness condition on mappings.The full text is divided into three chapters:In Chapter 1,Firstly,this thesis state the research background and signifi-cance and the present situation at home and abroad on the split equality fixed point problem,and then briefly describes its the research content and main inno-vation points.In Chapter 2,In Hilbert spaces,to study the iterative algorithm and it-s convergence theorems of the SEFPP for total asymptotically strictly pseudo-contractive mappings.The weak convergence theorem and the strong convergence theorem of an iterative algorithm proposed are obtained.In Chapter 3,In Hilbert spaces,to study the strong convergence theorem of the SEFPP for total asymptotically strictly pseudo-contractive mappings.The strong convergence theorem of an new iterative algorithm by the method of the hybrid projection proposed under the assumption of semi-compactness conditions on mappings is also obtained.In addtion,the results extend and apply to the mixed equilibrium problem and the variational inclusion problem.