On the Local Convergence of Two-Step Newton Type Method in Banach Spaces under Generalized Lipschitz Conditions

Akanksha Saxena, Ioannis K. Argyros, Jai P. Jaiswal, Christopher Argyros and Kamal R. Pardasani
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Akanksha Saxena: Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, M.P., India
Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Jai P. Jaiswal: Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur 495009, C.G., India
Christopher Argyros: Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA
Kamal R. Pardasani: Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, M.P., India

Mathematics, 2021, vol. 9, issue 6, 1-20

Abstract: The motive of this paper is to discuss the local convergence of a two-step Newton-type method of convergence rate three for solving nonlinear equations in Banach spaces. It is assumed that the first order derivative of nonlinear operator satisfies the generalized Lipschitz i.e., L -average condition. Also, some results on convergence of the same method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L -average particularly it is assumed that L is positive integrable function but not necessarily non-decreasing. Our new idea gives a tighter convergence analysis without new conditions. The proposed technique is useful in expanding the applicability of iterative methods. Useful examples justify the theoretical conclusions.

Keywords: banach space; nonlinear problem; local convergence; lipschitz condition; L-average; convergence ball (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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