The Strong Convergence Theorems Of λ Strict Pseudo-contractive Mappings

Since the strictly pseudocontractive mappings were proved by Browder in1967,the problem of constructing different iterative methods to study the convergenceproblem is becoming more and more extensive. After that, people have been studyingto approximate to the fixed points of strictly pseudocontractive mappings by usingdifferent iterative sequences such as modified Mann iterative and Ishikawa iterative,implicit and projection iteration etc in Hilbert space and Banach space.The results havebeen maded more considerable achievements.We continue to study the convergence theorem of λstrictly pseudocontractivemappings in pseudocontractive mappings under some restrictive conditions in Hilbertspace and Banach space.In chapter1,we discuss the significance and purpose of this paper. Furthermore,we present some research situations about the problem of domestic and foreign countryand we also give a summary of this work.The second chapter, we discuss the problem of approximating to the commonfixed point of finite λ demicontractive mappings under some restrictive conditions inBanach space.The third chapter, we discuss the Mann iterative which was constructed inHilbert space approximate to the P_F(T) x0of λ strictly pseudocontractive mappingsunder some restrictive conditions.The fourth chapter, in the Banach space,we discuss the implicit iterative sequencewith errors approximate to the fixed points of λ strictly pseudocontractive mappingsunder some restrictive conditions.The innovation of this thesis lies in the2-th,3-th,4-th chapter.