On the convergence of secant-like algorithms with applications to generalized fractional calculus

DOI10.4064/AM2275-12-2015zbMath1356.65144OpenAlexW2546856357MaRDI QIDQ2833630

Ioannis K. Argyros, George A. Anastassiou

Publication date: 18 November 2016

Published in: Applicationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/am2275-12-2015

zbMATH Keywords

semilocal convergenceBanach spacefractional calculussecant methodnonlinear operator equationsgeneralized fractional derivatives

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fractional derivatives and integrals (26A33) Numerical solutions to equations with nonlinear operators (65J15)

Cites Work

• Different anomalies in a Jarratt family of iterative root-finding methods
• A new tool to study real dynamics: the convergence plane
• Fractional representation formulae and right fractional inequalities
• Chaotic dynamics of a third-order Newton-type method
• Newton-type methods of high order and domains of semilocal and global convergence
• Third-order iterative methods under Kantorovich conditions
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• Convergence and Applications of Newton-type Iterations
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