Convergence of the Newton-Type Method for Generalized Equations

Authors

  • MH Rashid Department of Mathematics, Faculty of Science, University of Rajshahi Rajshahi-6205
  • A Sarder Department of Mathematics, Faculty of Science, University of Rajshahi Rajshahi-6205

DOI:

https://doi.org/10.3329/ganit.v35i0.28565

Keywords:

Set-valued mapping, Generalized equation, Local convergence, Pseudo-Lipschitz mapping, Newton-type method

Abstract

Let X and Y be real or complex Banach spaces. Suppose that f: X->Y is a Frechet differentiable function and F: X => 2Yis a set-valued mapping with closed graph. In the present paper, we study the Newton-type method for solving generalized equation 0 ? f(x) + F(x). We prove the existence of the sequence generated by the Newton-type method and establish local convergence of the sequence generated by this method for generalized equation.

GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 27-40

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Author Biography

MH Rashid, Department of Mathematics, Faculty of Science, University of Rajshahi Rajshahi-6205



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Published

2016-06-28

How to Cite

Rashid, M., & Sarder, A. (2016). Convergence of the Newton-Type Method for Generalized Equations. GANIT: Journal of Bangladesh Mathematical Society, 35, 27–40. https://doi.org/10.3329/ganit.v35i0.28565

Issue

Vol. 35 (2015)

Section

Articles

License

The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)