Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces

Year 2019, Volume: 2 Issue: 2, 121 - 128, 27.06.2019

İoannis K Argyros Santhosh George

https://doi.org/10.33434/cams.507917

https://izlik.org/JA65SK84RH

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.
• [11] I. K. Argyros, On a quadratically convergent iterative method using divided differences of order one, J. Korean. Math. S. M. E. Ser. B, 14 (3) (2007), 203-221.
• [12] W. C. Rheinboldt, An adaptive continuation process for solving systems of nonlinear equations, Banach Center Publ., 3 (1977), 129-142.
• [13] J. F. Traub, Iterative Methods for the Solution of Equations, Prentice Hall Englewood Cliffs, New Jersey, USA, 1994.