On the convergence and data dependence results for multistep Picard-Mann iteration process in the class of contractive-like operators
نویسندگان
چکیده
منابع مشابه
Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
The purpose of this paper is to introduce a new class of quasi-contractive operators and to show that the most used fixed point iterative methods, that is, the Picard and Mann iterations, are convergent to the unique fixed point. The comparison of these methods with respect to their convergence rate is obtained.
متن کاملPicard Iteration Converges Faster than Mann Iteration for a Class of Quasi-contractive Operators
In the last three decades many papers have been published on the iterative approximation of fixed points for certain classes of operators, using the Mann and Ishikawa iteration methods, see [4], for a recent survey. These papers were motivated by the fact that, under weaker contractive type conditions, the Picard iteration (or the method of successive approximations), need not converge to the f...
متن کاملOn the Convergence of the Three-step Iteration Process in the Class of Quasi-contractive Operators
We establish a general theorem to approximate fixed points of quasi-contractive operators on a normed space through the three-step iteration process. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1].
متن کاملOn the Convergence of the Ishikawa Iteration in the Class of Quasi Contractive Operators
A convergence theorem of Rhoades [18] regarding the approximation of fixed points of some quasi contractive operators in uniformly convex Banach spaces using the Ishikawa iterative procedure, is extended to arbitrary Banach spaces. The conditions on the parameters {αn} that define the Ishikawa iteration are also weakened.
متن کاملSome Convergence Results for the Jungck-mann and the Jungck-ishikawa Iteration Processes in the Class of Generalized Zamfirescu Operators
In this paper, we shall establish some strong convergence results for the recently introduced Jungck-Mann iteration process of Singh et al. [18] and the newly introduced Jungck-Ishikawa iteration process in the class of non-selfmappings in an arbitrary Banach space. Our results are generalizations and extensions of those of Berinde [4], Rhoades [13, 14] as well as some other analogous ones in t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Sciences and Applications
سال: 2016
ISSN: 2008-1901
DOI: 10.22436/jnsa.009.06.27