On the Semilocal Convergence of the Multi–Point Variant of Jarratt Method: Unbounded Third Derivative Case

Zhang Yong, Neha Gupta, J. P. Jaiswal and Kalyanasundaram Madhu
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Zhang Yong: School of Mathematics and Physics, Changzhou University, Changzhou 213164, China
Neha Gupta: Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, India
J. P. Jaiswal: Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, India
Kalyanasundaram Madhu: Department of Mathematics, Saveetha Engineering College, Chennai 602105, India

Mathematics, 2019, vol. 7, issue 6, 1-14

Abstract: In this paper, we study the semilocal convergence of the multi-point variant of Jarratt method under two different mild situations. The first one is the assumption that just a second-order Fréchet derivative is bounded instead of third-order. In addition, in the next one, the bound of the norm of the third order Fréchet derivative is assumed at initial iterate rather than supposing it on the domain of the nonlinear operator and it also satisfies the local ω -continuity condition in order to prove the convergence, existence-uniqueness followed by a priori error bound. During the study, it is noted that some norms and functions have to recalculate and its significance can be also seen in the numerical section.

Keywords: Banach space; semilocal convergence; ω-continuity condition; Jarratt method; error bound (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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