1. A Third Order Newton-Like Method and Its Applications.
- Author
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Sahu, D. R., Agarwal, Ravi P., and Singh, Vipin Kumar
- Subjects
- *
STOCHASTIC convergence , *APPROXIMATION theory , *NONLINEAR operator equations , *BANACH spaces , *INTEGRAL equations , *FIXED point theory - Abstract
In this paper, we design a new third order Newton-like method and establish its convergence theory for finding the approximate solutions of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis of our third order Newton-like method under the ω -continuity condition. Then we apply our approach to solve nonlinear fixed point problems and Fredholm integral equations, where the first derivative of an involved operator does not necessarily satisfy the Hölder and Lipschitz continuity conditions. Several numerical examples are given, which compare the applicability of our convergence theory with the ones in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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