Semilocal convergence of a modified multi-point Jarratt method in Banach spaces under general continuity condition |
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Authors: | Xiuhua Wang Jisheng Kou |
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Institution: | 1. School of Mathematics and Statistics, Xiaogan University, Xiaogan, 432100, Hubei, China
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Abstract: | The semilocal convergence for a modified multi-point Jarratt method for solving non-linear equations in Banach spaces is established with the third-order Fréchet derivative of the operator under a general continuity condition. The recurrence relations are derived for the method, and from this, we prove an existence-uniqueness theorem, and give a priori error bounds. The R-order of the method is also analyzed with the third-order Fréchet derivative of the operator under different continuity conditions. Numerical application on non-linear integral equation of the mixed type is given to show our approach. |
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