Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces
Joint Authors
Gupta, D. K.
Kumar, Abhimanyu
Singh, Sukhjit
Martínez, Eulalia
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-05-07
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
The semilocal and local convergence analyses of a two-step iterative method for nonlinear nondifferentiable operators are described in Banach spaces.
The recurrence relations are derived under weaker conditions on the operator.
For semilocal convergence, the domain of the parameters is obtained to ensure guaranteed convergence under suitable initial approximations.
The applicability of local convergence is extended as the differentiability condition on the involved operator is avoided.
The region of accessibility and a way to enlarge the convergence domain are provided.
Theorems are given for the existence-uniqueness balls enclosing the unique solution.
Finally, some numerical examples including nonlinear Hammerstein type integral equations are worked out to validate the theoretical results.
American Psychological Association (APA)
Kumar, Abhimanyu& Gupta, D. K.& Martínez, Eulalia& Singh, Sukhjit. 2018. Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces. Complexity،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1135748
Modern Language Association (MLA)
Kumar, Abhimanyu…[et al.]. Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces. Complexity No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1135748
American Medical Association (AMA)
Kumar, Abhimanyu& Gupta, D. K.& Martínez, Eulalia& Singh, Sukhjit. Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces. Complexity. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1135748
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1135748