Local Convergence of the Chord Method for Generalized Equations
[1]
M. H. Rashid, Department of Mathematics, Faculty of Science, University of Rajshahi, Rajshahi, Bangladesh.
[2]
A. Basak, Department of Mathematics, Faculty of Science, University of Rajshahi, Rajshahi, Bangladesh.
[3]
M. Z. Khaton, Department of Mathematics, Sapahar Government Degree College, Naogaon, Bangladesh.
Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f : X ⟼ Y is a Frechet differentiable function and F : X→ 2Y is a set-valued mapping with closed graph. In the present paper, we study the Chord method for solving generalized equation 0 ∈ f(x)+ F(x). We prove the existence of the sequence generated by the Chord method and establish local convergence of the sequence generated by this method for generalized equation.
Chord Method, Generalized Equation, Local Convergence, Pseudo-Lipschitz Mapping, Set-Valued Mapping
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