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

Yıl 2019, Cilt: 2 Sayı: 2, 121 - 128, 27.06.2019

İoannis K Argyros Santhosh George

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

Öz

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.

Anahtar Kelimeler

Banach spaces Local convergence Newton-Kurchatov-type method Non-differentiable equations

Kaynakça

  • [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.

Yıl 2019, Cilt: 2 Sayı: 2, 121 - 128, 27.06.2019

İoannis K Argyros Santhosh George

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

Öz

Kaynakça

  • [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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

İoannis K Argyros 0000-0002-9189-9298

Santhosh George 0000-0002-3530-5539

Yayımlanma Tarihi 27 Haziran 2019
Gönderilme Tarihi 4 Ocak 2019
Kabul Tarihi 28 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 2

Kaynak Göster

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. Haziran 2019;2(2):121-128. doi:10.33434/cams.507917
Chicago Argyros, İoannis K, ve 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, sy. 2 (Haziran 2019): 121-28. https://doi.org/10.33434/cams.507917.
EndNote Argyros İK, George S (01 Haziran 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 ve S. George, “Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces”, Communications in Advanced Mathematical Sciences, c. 2, sy. 2, ss. 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 (Haziran 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 ve Santhosh George. “Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces”. Communications in Advanced Mathematical Sciences, c. 2, sy. 2, 2019, ss. 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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