Extended Newton-type Method for Generalized Equations with Hölderian Assumptions

In the present paper, we consider generalized equation $0\in f(x)+g(x)+\mathcal F(x)$, where $f:\mathcal X\to \mathcal Y$ is Fr\'{e}chet differentiable on a neighborhood $\Omega$ of point $\bar{x}$ in $\mathcal X$, $g:\mathcal at and linear as well F$ set-valued mapping with closed graph acting between two Banach spaces X$ Y$. We study above help extended Newton-type method, introduced [ M. Z. Khaton, H. Rashid, I. Hossain, Convergence Properties Iteration Method for Generalized Equations, Journal Mathematics Research, 10 (4) (2018), 1--18, DOI:10.5539/jmr.v10n4p1, under weaker conditions than that are used Khaton et al. (2018). Indeed, semilocal local convergence analysis provided this method Frechet derivative $f$ first-order divided difference $g$ Hölder continuous $\Omega$. particular, show converges superlinearly these results extend improve corresponding Argyros (2008) $et$ $al.$