Displaying similar documents to “A new convergence theorem for Steffensen's method on Banach spaces and applications.”

Local convergence of two competing third order methods in Banach space

Ioannis K. Argyros, Santhosh George (2014)

Applicationes Mathematicae

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We present a local convergence analysis for two popular third order methods of approximating a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for both methods under the same conditions. A comparison is given between the two methods, as well as numerical examples.

Local convergence comparison between two novel sixth order methods for solving equations

Santhosh George, Ioannis K. Argyros (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples...

Inertial forward-backward splitting method in Banach spaces with application to compressed sensing

Prasit Cholamjiak, Yekini Shehu (2019)

Applications of Mathematics

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We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces. ...

On the Halley method in Banach spaces

Ioannis K. Argyros, Hongmin Ren (2012)

Applicationes Mathematicae

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We provide a semilocal convergence analysis for Halley's method using convex majorants in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our results reduce and improve earlier ones in special cases.