Results on the Chebyshev method in banach spaces


  • Ioannis K. Argyros Cameron University.
  • Dong Chen University of Arkansas.



Numerical Solutions of Nonlinear operator equations, Banach spaces, Chebyshev iterative method, Kantorovich-type convergence, Newton-Kantorovich assumptions, Error bound expression


In this paper, under standard Newton-Kantorovich conditions, we establish the Kantorovich-type convergence theorem for Chebyshev method in Banach spaces.

Author Biographies

Ioannis K. Argyros, Cameron University.

Department of Mathematics.

Dong Chen, University of Arkansas.

Department of Mathematical Sciences.


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[3] Chen, D.: Standard Kantorovich theorem of the Chebyshev method on complex plane. Intern. J. Computer Math., 42:(1+2) (1993), 67-70.

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[6] Ostrowski, A.M.: Solution of Equations in Euclidean and Banach Spaces. Academic Press, New York, 3rd ed., 1973.

[7] Rall, L.B.: Computational Solution of Nonlinear Operator Equations. John Wiley & sons, Inc., New York, 1969.

[8] Yamamoto, T.: On the methos of Tangent Hyperbolas in Banach Spaces. J. Computational and Applied Math., 21(1988), 75-88.



How to Cite

I. K. Argyros and D. Chen, “Results on the Chebyshev method in banach spaces”, Proyecciones (Antofagasta, On line), vol. 12, no. 2, pp. 119-128, Apr. 2018.




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