Corrigendum to "Strong convergence of the modified Ishikawa iterative method for infinitely many nonexpansive mappings in Banach spaces" [Comput. Math. Appl 59 (2010) 1473-1483]

نویسندگان

  • Phayap Katchang
  • Poom Kumam
چکیده

In this communication we give the following corrigendum for the paper ‘‘Strong convergence of the modified Ishikawa iterativemethod for infinitelymany nonexpansivemappings in Banach spaces’’ [Comput. Math. Appl. 59 (2010) 1473–1483, doi: 10.1016/j.camwa.2010.01.025]: The conditions (ii) in Theorem3.1 should be revised to 0 < lim infn→∞ βn ≤ lim supn→∞ βn < 1 and (γn(1+βn)−2βn) > a for some a ∈ (0, 1). Also assume that subset C is such that C + C ⊂ C . The proof on page 1480, lines 23–27, should have the following inserted: ‖xn − Wnxn‖ ≤ ‖xn − yn‖ + ‖yn − Wnzn‖ + ‖Wnzn − Wnxn‖

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings

In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space  with a uniformly G$hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(ell_{p})$ spaces, $1 < p

متن کامل

Convergence theorems of multi-step iterative algorithm with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces

The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

متن کامل

A new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces

In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.

متن کامل

Weak and Strong Convergence of Finite Family with Errors of Nonexpansive Nonself-mappings

Let K be a subset of a real normed linear space E and let T be a self-mapping on K . T is said to be nonexpansive provided ‖Tx−Ty‖ ‖x− y‖ for all x, y ∈ K . Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spa...

متن کامل

Convergence and Stability of Modified Random SP-Iteration for A Generalized Asymptotically Quasi-Nonexpansive Mappings

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Computers & Mathematics with Applications

دوره 61  شماره 

صفحات  -

تاریخ انتشار 2011