Journal of Advances in Applied Mathematics

Download PDF (595.1 KB) PP. 91 - 108 Pub. Date: July 1, 2018

DOI: 10.22606/jaam.2018.33003

• Mohammed Harunor Rashid^*
  Department of Mathematics, Faculty of Science, University of Rajshahi, Rajshahi-6205, Bangladesh
• Md. Zulfikar Ali
  Department of Mathematics, Faculty of Science, University of Rajshahi, Rajshahi-6205, Bangladesh
• Alain Piétrus
  Département de Mathématiques, et Informatique, Université des Antilles et de la Guyane, Campus de Fouillole, F-97159 Pointe-à-Pitre, France.

Let X and Y be Banach spaces. Let be an open subset of X. Suppose that f : X ! Y is Fréchet differentiable in and F : X  2Y is set-valued mapping with closed graph. In the present paper, for solving the generalized equations 0 2 f(x) + F(x), an extended cubic method (ECM) is introduced and studied its convergence analysis. Indeed, we analyze semi-local and local convergence of the ECM.

Generalized equations, set-valued mappings, Lipschitz–like mappings, cubic method, semi-local convergence.

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