A Relationship between the Lipschitz Constants Appearing in Taylor`s Formula

Hong Min Ren; Ioannis K. Argyros

한국수학교육학회 이론수학과 교직수학 A Relationship between the Lipschitz Constants Appearing in Taylor`s Formula

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( Ioannis K. Argyros ) , ( Hong Min Ren )

한국수학교육학회 2011.11

이론수학과 교직수학 vol. 18 iss. 4 345-351(7pages)

UCI I410-ECN-0102-2012-370-002606157

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Abstract

Taylor`s formula is a powerful tool in analysis. In this study, we assume that an operator is m-times Frechet-differentiable and satisfies a Lipschitz condition. We then obtain some Taylor formulas using only the Lipschitz constants. Applications are also provided.

Keywords

Taylor`s formula

Frechet-differentiable operator

iterative processes

Banach space

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