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Ball convergence for combined three-step methods under generalized conditions in banach space
ArticleAbstract: We give a local convergence analysis for an eighth-order convergent method in order to approximate aPalabras claves:Banach space, Iterative method, Lipschitz constant, local convergence, Order of convergenceAutores:Argyros I.K., Behl R., Daniel González, Motsa S.S.Fuentes:scopusA Semilocal Convergence for a Uniparametric Family of Efficient Secant-Like Methods
ArticleAbstract: We present a semilocal convergence analysis for a uniparametric family of efficient secant-like methPalabras claves:Autores:Argyros I.K., Daniel González, Magreñán A.A.Fuentes:scopusA semilocal convergence result for Newton's method under generalized conditions of Kantorovich
ArticleAbstract: From Kantorovich's theory we establish a general semilocal convergence result for Newton's method baPalabras claves:A priori error estimates, Conservative problem, Majorizing sequence, Newton's method, semilocal convergence, The Newton-Kantorovich theoremAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopusA variant of the Newton-Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type
ArticleAbstract: We study nonlinear integral equations of mixed Hammerstein type using Newton's method as follows. WePalabras claves:Bratu's equation, Hammerstein's equation, Kantorovich's theorem, Majorizing sequence, Newton's method, semilocal convergenceAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopusConvergence and dynamics of a higher-order method
ArticleAbstract: Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, anPalabras claves:convergence, Dynamics, High-order iterative methodAutores:Argyros I.K., Daniel González, Magreñán A.A., Moysi A., Regmi S., Sicilia J.A.Fuentes:scopusExtended Multi-Step Jarratt-like Schemes of High Order for Equations and Systems
ArticleAbstract: The local convergence analysis of multi-step, high-order Jarratt-like schemes is extended for solvinPalabras claves:Banach space, derivative-free, Jarratt scheme, local convergence, multi-step schemeAutores:Argyros C., Argyros I.K., Argyros M., Daniel González, Johan CeballosFuentes:scopusExtending the applicability of Newton's method for a class of boundary value problems using the shooting method
ArticleAbstract: We use Newton's method to approximate locally unique solutions for a class of boundary value problemPalabras claves:boundary value problem, Lipschitz condition, Newton's method, Shooting methodAutores:Argyros I.K., Daniel González, Gutiérrez J.M., Johan CeballosFuentes:scopusExtending the applicability of Newton's method for k-Fréchet differentiable operators in Banach spaces
ArticleAbstract: We extend the applicability of Newton's method for k-Fréchet differentiable operators in a Banach spPalabras claves:A priori error estimates, Hammerstein integral equation, Majorizing sequence, Newton's method, semilocal convergence, The Newton-Kantorovich theoremAutores:Argyros I.K., Daniel GonzálezFuentes:scopusExtending the usage of Newton's method with applications to the solution of Bratu's equation
ArticleAbstract: We use Newton's method to solve previously unsolved problems, expanding the applicability of the metPalabras claves:Bratu, convergence, NewtonAutores:Argyros I.K., Daniel GonzálezFuentes:scopusMajorizing sequences for Newton's method from initial value problems
ArticleAbstract: The most restrictive condition used by Kantorovich for proving the semilocal convergence of Newton'sPalabras claves:Bratu's equation, Kantorovich's technique, Majorizing sequence, Newton's method, Order of convergence, semilocal convergenceAutores:Daniel González, Ezquerro J., Hernández-Verón M.Fuentes:scopus