Convergence analysis of a variant of Newton-type method for generalized equations
Mohammed Harunor RASHİD · International Journal of Computer Mathematics · 2017
Let X and Y be Banach spaces. Consider the following generalized equation problem: (1) 0∈f(x)+F(x),(1) where f is Fréchet differentiable on an open subset Ω of X and F is set-valued mapping with closed graph acting between Banach spaces. In the present paper, we introduce a variant of Newton-type method for solving generalized equation (1). Semi-local and local convergence analysis are provided under the weaker condition that of utilized by Jean-Alexis and Pietrus [A variant of Newton's method for generalized equations, Rev. Colombiana Mat. 39 (2005), pp. 97–112]. In particular, this result extends the corresponding ones Jean-Alexis and Pietrus (2005). Finally, we present a numerical example to validate the convergence result of this method.