Convergence for iterative methods on Banach spaces of a convergence structure with applications to fractional calculus

DOI10.1007/s40324-015-0044-yzbMath1400.65028OpenAlexW1121636316MaRDI QIDQ890782

George A. Anastassiou, Ioannis K. Argyros

Publication date: 13 November 2015

Published in: S\(\vec{\text{e}}\)MA Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40324-015-0044-y

zbMATH Keywords

semilocal convergenceNewton-like methodfractional Caputo derivativeBanach space with a convergence structurefractional Taylor formula

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Fractional derivatives and integrals (26A33) Numerical solutions to equations with nonlinear operators (65J15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Different anomalies in a Jarratt family of iterative root-finding methods
• A new tool to study real dynamics: the convergence plane
• Intelligent mathematics: computational analysis
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• 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
• Fractional Differentiation Inequalities
• A unifying theorem on newton's method