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| Existence and Uniqueness Theorems for a Three-step Newton-type Method under $L$-Average Conditions |
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| KeyWord:Banach space Nonlinear equation Lipschitz condition $L$-average Convergence ball |
| Author Name | Affiliation | | Jai Prakash Jaiswal | Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur, C.G., India-495009
Faculty of Science, Barkatullah University, Bhopal, M.P.-462026, India
Regional Institute of Education, Bhopal, M.P.-462013, India |
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| Abstract: |
| In this paper, we study the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weaker hypothesis. More precisely, we derive the existence and uniqueness theorems, when the first-order derivative of nonlinear operator satisfies the $L$-average conditions instead of the usual Lipschitz condition, which have been discussed in the earlier study. |
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