Ball convergence theorems for Halley’s method in Banach space

被引：0
|
作者：
Ioannis K. Argyros
Hongmin Ren
机构：
[1] Cameron University,Department of Mathematical Sciences
[2] Hangzhou Polytechnic,College of Information and Electronics
来源：
Journal of Applied Mathematics and Computing | 2012年 / 38卷 / 1-2期
关键词：
Newton’s method; Halley’s method; Banach space; Ball convergence; Convex majorants; Radius of convergence; 65G99; 65J15; 47H17; 47J05; 49M15;
D O I：
10.1007/s12190-011-0490-3
中图分类号：
学科分类号：
摘要：
We provide local convergence results for Halley’s method in order to approximate a locally unique zero of an operator in a Banach space setting using convex majorants. Kantorovich-type and Smale-type results are considered as applications and special cases.
引用
收藏
页码：453 / 465
页数：12
相关论文
共 50 条
  • [21] Convergence theorems of a new multiparametric family of Newton-like method in Banach space
    Kumari, Chandni
    Parida, P. K.
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2021, 12 (02): : 335 - 362
  • [22] Convergence of Halley's method for operators with the bounded second Frechet-derivative in Banach spaces
    Argyros, Ioannis K.
    Cho, Yeol Je
    Ren, Hongmin
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
  • [23] Strong convergence theorems for relatively nonexpansive mappings in a Banach space
    Qin, Xiaolong
    Su, Yongfu
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (06) : 1958 - 1965
  • [24] Vitali Type Convergence Theorems for Banach Space Valued Integrals
    Balcerzak, Marek
    Musia, Kazimierz
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (11) : 2027 - 2036
  • [25] Convergence theorems of iterations for a pair of nonexpansive mappings in a Banach space
    Tamura, T
    FUNCTION SPACES, PROCEEDINGS, 2000, 213 : 497 - 505
  • [26] The Convergence Theorems of Set-Valued Pramart in a Banach Space
    Guan, Li
    Li, Shoumei
    NONLINEAR MATHEMATICS FOR UNCERTAINTY AND ITS APPLICATIONS, 2011, 100 : 135 - 142
  • [27] Vitali Type Convergence Theorems for Banach Space Valued Integrals
    Marek BALCERZAK
    Kazimierz MUSIAL
    Acta Mathematica Sinica,English Series, 2013, (11) : 2027 - 2036
  • [28] Vitali type convergence theorems for Banach space valued integrals
    Marek Balcerzak
    Kazimierz Musiał
    Acta Mathematica Sinica, English Series, 2013, 29 : 2027 - 2036
  • [29] Ball Convergence for Second Derivative Free Methods in Banach Space
    Argyros I.K.
    Jidesh P.
    George S.
    International Journal of Applied and Computational Mathematics, 2017, 3 (2) : 713 - 720
  • [30] Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
    Alberto Magreñán Á.
    Argyros I.K.
    SeMA Journal, 2015, 71 (1) : 39 - 55
12345