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

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.

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.
Year 2019, Volume: 2 Issue: 2, 121 - 128, 27.06.2019
https://doi.org/10.33434/cams.507917

Abstract

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.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

İoannis K Argyros This is me 0000-0002-9189-9298

Santhosh George 0000-0002-3530-5539

Publication Date June 27, 2019
Submission Date January 4, 2019
Acceptance Date March 28, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA 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.

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