The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval

DOI10.1016/j.jmaa.2005.11.058zbMath1101.47056OpenAlexW2049067269MaRDI QIDQ855456

Qing Yuan, Qihou Liu

Publication date: 7 December 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.11.058

zbMATH Keywords

fixed pointIshikawa iterationreal function

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Iteration of real functions in one variable (26A18)

Related Items

Rate of convergence of Mann, Ishikawa and Noor iterations for continuous functions on an arbitrary interval ⋮ Strong convergence theorems and rate of convergence of multi-step iterative methods for continuous mappings on an arbitrary interval ⋮ On the rate of convergence of P-iteration, SP-iteration, and D-iteration methods for continuous nondecreasing functions on closed intervals ⋮ Convergence theorems for continuous functions on an arbitrary interval ⋮ Approximating fixed points for continuous functions on an arbitrary interval ⋮ Fixed point problems of the Picard-Mann hybrid iterative process for continuous functions on an arbitrary interval ⋮ On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval ⋮ On the convergence of an iteration method for continuous mappings on an arbitrary interval

Cites Work

• Fixed point iterations for real functions
• Fixed Points by a New Iteration Method
• Mean Value Methods in Iteration