Advanced search
Publication Cover
Cogent Mathematics Volume 2, 2015 - Issue 1
Submit an article Journal homepage
679
Views
6
CrossRef citations to date
0
Altmetric
Research Article

Local convergence for deformed Chebyshev-type method in Banach space under weak conditions

Ioannis K. ArgyrosDepartment of Mathematical Sciences, Cameron University, Lawton, OK73505USACorrespondence[email protected]
View further author information
&
Santhosh GeorgeDepartment of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangaluru, Karnataka757 025IndiaView further author information
|
Yong Hong WuCurtin University, AustraliaView further author information
(Reviewing Editor)
Article: 1036958 | Received 12 Oct 2014, Accepted 16 Mar 2015, Published online: 28 Apr 2015

References

  • Amat, S., Busquier, S., & Gutiérrez, J. M. (2003). Geometric constructions of iterative functions to solve nonlinear equations. Journal of Computational and Applied Mathematics, 157, 197–205.
  • Argyros, I. K. (1985). Quadratic equations and applications to Chandrasekhar’s and related equations. Bulletin of the Australian Mathematical Society, 32, 275–292.
  • Argyros, I. K. (2004). A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach spaces. Journal of Mathematical Analysis and Applications, 20, 373–397.
  • Argyros, I. K. (2007). Studies in computational mathematics. In C. K. Chui & L. Wuytack (Eds.), Computational theory of iterative methods (Chap. 15). New York, NY: Elsevier.
  • Argyros, I. K., & Hilout, S. (2012). Weaker conditions for the convergence of Newton’s method. Journal of Complexity, 28, 364–387.
  • Argyros, I. K., & Hilout, S. (2013). Numerical methods in nonlinear analysis. London: World Scientific Publishing.
  • Candela, V., & Marquina, A. (1990a). Recurrence relations for rational cubic methods I: The Halley method. Computing, 44, 169–184.
  • Candela, V., & Marquina, A. (1990b). Recurrence relations for rational cubic methods II: The Chebyshev method. Computing, 45, 355–367.
  • Chun, C., Stanica, P., & Neta, B. (2011). Third order family of methods in Banach spaces. ComputersandMathematicswithApplications, 61, 1665–1675.
  • Gutiérrez, J. M., & Hernández, M. A. (1997). Third-order iterative methods for operators with bounded second derivative. Journal of Computational and Applied Mathematics, 82, 171–183.
  • Gutiérrez, J. M., & Hernández, M. A. (1998). Recurrence relations for the super-Halley method. Computers & Mathematics with Applications, 36, 1–8.
  • Hernández, M. A. (2001). Chebyshev’s approximation algorithms and applications. Computers & Mathematics with Applications, 41, 433–455.
  • Hernández, M. A., & Salanova, M. A. (2000). Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method. Journal of Computational and Applied Mathematics, 126, 131–143.
  • Kantorovich, L. V., & Akilov, G. P. (1982). Functional analysis. Oxford: Pergamon Press.
  • Ortega, J. M., & Rheinboldt, W. C. (1970). Iterative solution of nonlinear equations in several variables. New York, NY: Academic Press.
  • Parida, P. K., & Gupta, D. K. (2008). Recurrence relations for semi-local convergence of a Newton-like method in Banach spaces. Journal of Mathematical Analysis and Applications, 345, 350–361.
  • Wu, Q., & Zhao, Y. (2007). Newton–Kantorovich type convergence theorem for a family of new deformed Chebyshev method. Applied Mathematics and Computation, 192, 405–412.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.