Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces
Abstract
We provide a new local convergence analysis of a Newton-Kurchatov-like method to solve non-differentiable equations in Banach spaces. Our result improve the earlier works in literature. The examples were used to test our hypotheses.
Keywords
Banach spaces,Local convergence,Newton-Kurchatov-type method,Non-differentiable equations
References
- [1] I. K. Argyros, Computational theory of iterative methods, Series: Studies in Computational Mathematics 15, C.K. Chui and L. Wuytack (editors), Elservier Publ. Co. New York, USA, 2007.
- [2] J.M. Ortega, W.C. Rheinbolt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
- [3] I. K. Argyros, On the Secant method, Publ. Math. Debrecen, 43 (1993), 223-238.
- [4] F. A. Potra, V. Pt´ak, Nondiscrete Induction and Iterative Methods, Pitman Publishing Limited, London, 1984.
- [5] V. A. Kurchatov, On the method of linear interpolation for the solution of functional equations, (Russion) Dolk. Akad. Nauk SSSR, 1998 (1971) 524-526, translation in Soviet Math. Dolk., 12 (1971) 835-838.
- [6] I. K. Argyros, On the two point Newton-like methods of convergent R-order two, Int. J. Comput. Math., 82 (2005), 219-233.
- [7] I. K. Argyros, A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations, J. Math. Anal. Appl. 332 (2007), 97-108.
- [8] M. A. Hernandez, M. J. Rubio, On the local convergence of a Newton-Kurchatov-type method for non-differentiable operators, Appl. Math. Comput., 304 (2017), 1-9.
- [9] S. Shakhno, On the Secant method under generalized Lipschitz conditions for the divided operator, PAMM-Proc. Appl. Math. Mech., 7 (2007), 2060083-2060084.
- [10] A. Cordero, F. Soleymani, J. R. Torregrosa, F. K. Haghani, A family of Kurchatov-type methods and its stability, Appl. Math. Comput., 294 (2017), 264-279.
