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Outline

The Secant method for nondifferentiable operators

2002, Applied Mathematics Letters

https://doi.org/10.1016/S0893-9659(01)00150-1

Abstract

m this paper, we use the Secant method to find a solution of a nonlinear operator equation in Banach spaces. A semilocal convergence result is obtained. For that, we consider a condition for divided differences which generalizes the usual once, i.e., Lipschitz continuous or Hiilder continuous conditions. Besides, we apply our results to approximate the solution of a nonlinear equation.

References (6)

  1. F.A. Potra and V. Ptak, Nondismte Induction and Itemtive Processes, Pitman, (1984).
  2. I.K. Argyros, The Secant method and lixed points of nonlinear operators, Mh. Math. 106,85-Q4, (1988).
  3. I.K. Argyros, On an application of a variant of the clceed graph theorem and the Secant method, Z'amkang J. Math. 24, 251-267, (1993).
  4. I.K. Argyros, On the Secant method, Publ. Math. Debmcen 43 (3-4), 223-238, (1993).
  5. F.A. Potra, An application of the induction method of V. Pt& to the study of regula falsi, Aplikace Matem- ati.@ 26, 111-120, (1981).
  6. J.W. Schmidt, Ftegula-falsi verfahren mit konsistenter steigung und majoranten prinzip, Periodica Mathe- math Hungarica 6, 187-193, (1974).