Convergence of the family of the deformed Euler–Halley iterations under the Hölder condition of the second derivative

• Published in: Journal of computational and applied mathematics Vol. 194; no. 2; pp. 294 - 308
• Main Authors: Ye, Xintao, Li, Chong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2006; Elsevier
• Subjects: Exact sciences and technology; Mathematical analysis; Mathematics; Nonlinear algebraic and transcendental equations; Nonlinear operator equation; Numerical analysis; Numerical analysis in abstract spaces; Numerical analysis. Scientific computation; Operator theory; Sciences and techniques of general use; The family of the deformed Euler–Halley iterations; The Hölder condition; 47H10; The Hölder condition; 65H10; The family of the deformed Euler–Halley iterations; 65J15; Nonlinear operator equation; Operator equation; Euler Halley iteration; Iteration; Banach space; Convergence; Non linear operator; Non linear equation; Numerical analysis; Applied mathematics; Hammerstein equation; Integral equation; The Holder condition; The family of the deformed Euler-Halley iterations
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2005.07.019

The convergence problem of the family of the deformed Euler–Halley iterations with parameters for solving nonlinear operator equations in Banach spaces is studied. Under the assumption that the second derivative of the operator satisfies the Hölder condition, a convergence criterion of the order 2 + p of the iteration family is established. An application to a nonlinear Hammerstein integral equation of the second kind is provided.