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.
[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.
Year 2019,
Volume: 2 Issue: 2, 121 - 128, 27.06.2019
[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.
Argyros, İ. K., & George, S. (2019). Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces. Communications in Advanced Mathematical Sciences, 2(2), 121-128. https://doi.org/10.33434/cams.507917
AMA
Argyros İK, George S. Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces. Communications in Advanced Mathematical Sciences. June 2019;2(2):121-128. doi:10.33434/cams.507917
Chicago
Argyros, İoannis K, and Santhosh George. “Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces”. Communications in Advanced Mathematical Sciences 2, no. 2 (June 2019): 121-28. https://doi.org/10.33434/cams.507917.
EndNote
Argyros İK, George S (June 1, 2019) Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces. Communications in Advanced Mathematical Sciences 2 2 121–128.
IEEE
İ. K. Argyros and S. George, “Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces”, Communications in Advanced Mathematical Sciences, vol. 2, no. 2, pp. 121–128, 2019, doi: 10.33434/cams.507917.
ISNAD
Argyros, İoannis K - George, Santhosh. “Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces”. Communications in Advanced Mathematical Sciences 2/2 (June 2019), 121-128. https://doi.org/10.33434/cams.507917.
JAMA
Argyros İK, George S. Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces. Communications in Advanced Mathematical Sciences. 2019;2:121–128.
MLA
Argyros, İoannis K and Santhosh George. “Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces”. Communications in Advanced Mathematical Sciences, vol. 2, no. 2, 2019, pp. 121-8, doi:10.33434/cams.507917.
Vancouver
Argyros İK, George S. Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces. Communications in Advanced Mathematical Sciences. 2019;2(2):121-8.