Preprint Article Version 1 This version is not peer-reviewed

A Third Order Newton-Like Method and Its Applications

Version 1 : Received: 8 October 2018 / Approved: 9 October 2018 / Online: 9 October 2018 (03:43:45 CEST)

A peer-reviewed article of this Preprint also exists.

Sahu, D.R.; Agarwal, R.P.; Singh, V.K. A Third Order Newton-Like Method and Its Applications. Mathematics 2019, 7, 31. Sahu, D.R.; Agarwal, R.P.; Singh, V.K. A Third Order Newton-Like Method and Its Applications. Mathematics 2019, 7, 31.

Journal reference: Mathematics 2018, 7, 31
DOI: 10.3390/math7010031

Abstract

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

Subject Areas

nonlinear operator equations; Fréchet derivative; ω-continuity condition; the Newton like method; Frédholm integral equation