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Journal of Inequalities and Applications

, 2009:624631

First Online: 29 December 2009Received: 21 August 2009Revised: 05 November 2009Accepted: 06 November 2009


We shall introduce and construct explicitly the complementary Lidstone interpolating polynomial Open image in new window of degree Open image in new window, which involves interpolating data at the odd-order derivatives. For Open image in new window we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard-s, approximate Picard-s, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a Open image in new windowth order differential equation and the complementary Lidstone boundary conditions.

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Autor: Ravi P. Agarwal - Sandra Pinelas - Patricia J. Y. Wong


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