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Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions

Open Access
|Dec 2018

References

  1. [1] I. K. Argyros, Stirling’s method and fixed points of nonlinear operator equations in Banach spaces, Bull. Inst. Math. Acad. Sin. (N.S.)23, (1995), 13-20
  2. [2] I. K. Argyros, On The Convergence and Application of Stirling’s Method, Applicationes Mathematicae, 30, (2003), 109-11910.4064/am30-1-7
  3. [3] I. K. Argyros, A new iterative method of asymptotic order 1+2$1 + \sqrt 2 $ for the computation of fixed points, Int. J. Comput. Math.82, (2005), 1413-142810.1080/00207160500113546
  4. [4] I. K. Argyros, Computational Theory of Iterative Methods. Series: Studies in Computational Mathematics, 15, (2007)
  5. [5] I. K. Argyros and S. Hilout, Weaker conditions for the convergence of Newton’s method, Journal of Complexity, 28, (2012), 364-38710.1016/j.jco.2011.12.003
  6. [6] I. K. Argyros and A. A. Magreñán, Iterative Methods and Their Dynamics with Applications: A Contemporary Study, CRC Press, New York, 201710.1201/9781315153469
  7. [7] S. Maruster and S. George I. K. Argyros, On the Convergence of Stirling’s Method for Fixed Points Under Not Necessarily Contractive Hypotheses, International Journal of Applied and Computational Mathematics, 3, (2017), 1071-108110.1007/s40819-017-0401-x
  8. [8] I. K. Argyros and F. Szidarovszky, The Theory and Applications of Iteration Methods, CRC Press, Boca Raton, Florida, USA, 1993
  9. [9] R. G. Bartle, Newton’s method in Banach spaces, Proc. Amer. Math. Soc.6, (1955), 827-83110.1090/S0002-9939-1955-0071730-1
  10. [10] S. K. Parhi and S. Singh D. K. Gupta, Semilocal convergence of Stirling’s method for fixed points in Banach spaces, International Journal of Mathematics in Operational Research, 9, (2016), 243-25710.1504/IJMOR.2016.078003
  11. [11] M. A. Hernández, The Newton Method for Operators with Hölder Continuous First Derivative, Journal of Optimization Theory and Applications, 109, (2001), 631-64810.1023/A:1017571906739
  12. [12] L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982
  13. [13] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, SIAM, Philadelphia, 200010.1137/1.9780898719468
  14. [14] S. K. Parhi and D. K. Gupta, Semilocal convergence of Stirling’s method under Hölder continuous first derivative in Banach spaces, International Journal of Computer Mathematics, 87, (2010), 2752-275910.1080/00207160902777922
  15. [15] S. K. Parhi and D. K. Gupta, Relaxing convergence conditions for Stirling’s method, Mathematical methods in the Applied Sciences, 33, (2010), 224-23210.1002/mma.1164
  16. [16] S. K. Parhi and D. K. Gupta, Convergence of Stirling’s method under weak differentiability condition, Mathematical methods in the Applied Sciences, 34, (2011), 168-17510.1002/mma.1345
  17. [17] L. B. Rall, Computational Solution of Nonlinear Operator Equations, E. Robert Krieger, New York, 1969
  18. [18] L. B. Rall, Convergence of Stirling’s method in Banach spaces, Aequationes Math.12, (1975), 12-2010.1007/BF01834034
  19. [19] W. Werner, Newton-like methods for the computation of fixed points, Comput. Math. Appl.10, (1984), 77-8610.1016/0898-1221(84)90088-9
DOI: https://doi.org/10.2478/awutm-2018-0007 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 86 - 98
Submitted on: Nov 10, 2017
Accepted on: Jan 10, 2018
Published on: Dec 7, 2018
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2018 Ioannis K. Argyros, P.K. Parida, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.