Iterative Convergence For Fixed Points Of Nonlinear Operators And Solutions Of Equations

In this paper, we mainly study the convergence problem of fixed points for several classes of nonlinear operators and solution of equations. First, we establish equivalence theorem of convergence of modified lshikawa and Mann iterative sequences with errors for asymptotically nonexpansive mapping in intermediate sense and strictly asymptotically pseudoco-contractive mappings under the conditions of removing the bounded restrictions of { }nx and { }nnT x, and substituting()n ng =o a with the weaker condition0ng ®(n ® ￥) in real Banach spaces by using a new analytical technique. Next, we study iteractive convergence of fixed points for a class of j- strongly pseudo-contractive operator without continuity or even without boundedness in Hilbert space, where the condtion used,20()n n nax -Tx ®n ® ￥ is controllable. Then, we shudy convergence of the common solution for a finite family of j- strongly accretive operator equations in Banach spaces without any bounded assumption, and obtain a strong convergence theorem, at the same time, also give an example to show universality of the result of this paper.And then, we prove a sufficient and necessary condition for Ishikawa iterative sequence with mixed errors of two finite families generalized uniformly quasi-Lipschitz mapingsiT andiS(i =1, 2, ×××, N) to converge to common fixed point in Banach spaces,where D does not need to be bounded, andiT andiS do not need to be continueous.Finall,we introduce a new class of finite family generalized asymptoticallyj- hemi-contractive mappings. Strong convergence theorems of modified Ishikawa iterative sequence with mixed errors for non-Lipschitz finite family generalized asymptoticallyj- hemi-contractive mappings in normed linear spaces are establishied without any bounded assumption.The theorems obtained in this paper improve and extend some known results.