A generalized Kantorovich theorem on the solvability of nonlinear equations

• Autores: Livinus U. Uko, Ioannis K. Argyros
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 77, Nº. 1-2, 2009, págs. 99-106
• Idioma: inglés
• DOI: 10.1007/s00010-008-2950-x
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• Resumen

  • The Kantorovich theorem is a fundamental tool in nonlinear analysis for proving the existence and uniqueness of solutions of nonlinear equations arising in various fields. This theorem was weakened recently by Argyros who used a combination of Lipschitz and center-Lipschitz conditions in place of the Lipschitz conditions of the Kantorovich theorem. In the present paper we use the Argyros theorem to formulate a generalized Kantorovich theorem that enables us deduce the solvability of equations and the convergence of Newton�s method with minimal assumptions.