Convergence and Stability Analysis of a New Four-Step Fixed-Point Algorithm
Open Access
- 30 June 2022
- journal article
- Published by Aksaray University in Aksaray University Journal of Science and Engineering
- Vol. 6 (1), 57-70
- https://doi.org/10.29002/asujse.1096163
Abstract
The concept of stability is studied on many different types of mathematical structures. This concept can be thought of as the small changes that will be applied in the structure studied should not disrupt the functioning of this structure. In this context, we performed the convergence and stability analysis of the new four-step iteration algorithm that we defined in this study, under appropriate conditions. In addition, we execute a speed comparison with existing algorithms to prove that the new algorithm is effective and useful, and we gave a numerical example to support our result.Keywords
This publication has 23 references indexed in Scilit:
- Strong convergence theorems and rate of convergence of multi-step iterative methods for continuous mappings on an arbitrary intervalFixed Point Theory and Algorithms for Sciences and Engineering, 2012
- Some iterative methods for finding fixed points and for solving constrained convex minimization problemsNonlinear Analysis, 2011
- The Douglas–Rachford Algorithm in the Absence of ConvexityPublished by Springer Science and Business Media LLC ,2011
- Fixed point characterization of biological networks with complex graph topologyBioinformatics, 2010
- Data Dependence for Ishikawa Iteration When Dealing with Contractive-Like OperatorsFixed Point Theory and Applications, 2008
- A simple fixed‐point approach to invert a deformation fielda)Medical Physics, 2007
- Fixed point iteration for local strictly pseudo-contractive mappingProceedings of the American Mathematical Society, 1991
- The Round‐off Stability of IterationsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1967
- Zur Entwicklung des Stabilitätsbegriffes in der MechanikThe Science of Nature, 1959
- Über Abbildung von MannigfaltigkeitenMathematische Annalen, 1911