Convergence, stability, and data dependence of a new iterative algorithm with an application

DOI10.1007/s40314-020-01316-2zbMath1463.47204OpenAlexW3085530664MaRDI QIDQ827372

Faeem Ali, Javid Ali

Publication date: 7 January 2021

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-020-01316-2

zbMATH Keywords

fixed pointsstrong convergencedata dependenceweak contractionnonlinear quadratic Volterra integral equationnumerically stable\(F^*\) iterative algorithm

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15) Volterra integral equations (45D05) Fixed-point iterations (47J26)

Related Items (5)

Estimating fixed points via new iterative scheme with an application ⋮ Some convergence, stability, and data dependence results for $K^{\ast }$ iterative method of quasi-strictly contractive mappings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A comparative study on iterative algorithms of almost contractions in the context of convergence, stability and data dependency

Cites Work

• Convergence in norm of modified Krasnoselski-Mann iterations for fixed points of demicontractive mappings
• Fixed point theorems and stability results for fixed point iteration procedures
• A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings
• Iterative approximation of fixed points
• Data dependence for Ishikawa iteration when dealing with contractive-like operators
• Strong convergence of the modified Ishikawa iterative method for infinitely many nonexpansive mappings in Banach spaces
• Stability of the Mann and Ishikawa iteration procedures for \(\phi\)-strong pseudocontractions and nonlinear equations of the \(\phi\)-strongly accretive type
• Stability of the Ishikawa iteration method for quasi-contractive maps
• A note on the stability of iteration procedures for strong pseudocontractions and strongly accretive type equations
• Data dependence of the fixed point set of some multivalued weakly Picard operators.
• A stable iteration procedure for quasi-contractive maps
• Stability results for the Ishikawa fixed point iteration procedure
• Some observations on generalized non-expansive mappings with an application
• Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
• A Picard-Mann hybrid iterative process
• Monotonicity properties of the superposition operator and their applications
• Existence and data dependence of fixed points for multivalued operators on gauge spaces
• On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis
• Continuous Dependence of Fixed Point Sets
• Fixed Points by a New Iteration Method
• The Round‐off Stability of Iterations
• Mean Value Methods in Iteration
• Fixed point theorems in metric spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Convergence, stability, and data dependence of a new iterative algorithm with an application