Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces. (7th May 2018)

• Record Type: Journal Article
• Authors: Kumar, Abhimanyu; Gupta, Dharmendra K.; Martínez, Eulalia; Singh, Sukhjit
• Other Names: Comminiello Danilo Academic Editor.
• Is Part Of: Complexity. Volume 2018(2018)
• Publication Date: 2018-05-07
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2018/7352780
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : 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.