On Some Fixed Point Iterative Schemes with Strong Convergence and Their Applications
Open Access
- 20 March 2023
- journal article
- research article
- Published by MDPI AG in Mathematical and Computational Applications
- Vol. 28 (2), 45
- https://doi.org/10.3390/mca28020045
Abstract
In this paper, a new one-parameter class of fixed point iterative method is proposed to approximate the fixed points of contractive type mappings. The presence of an arbitrary parameter in the proposed family increases its interval of convergence. Further, we also propose new two-step and three-step fixed point iterative schemes. We also discuss the stability, strong convergence and fastness of the proposed methods. Furthermore, numerical experiments are performed to check the applicability of the new methods, and these have been compared with well-known similar existing methods in the literature.Keywords
Funding Information
- UGC (BININ01887801)
This publication has 16 references indexed in Scilit:
- A Picard-Mann hybrid iterative processFixed Point Theory and Algorithms for Sciences and Engineering, 2013
- Asymptotically Pseudocontractions, Banach Operator Pairs and Best Simultaneous ApproximationsFixed Point Theory and Applications, 2011
- Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive MappingsJournal of Optimization Theory and Applications, 2009
- Common fixed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach spaceJournal of Computational and Applied Mathematics, 2009
- Effect of temperature dependent properties on MHD convection of water near its density maximum in a square cavityInternational Journal of Thermal Sciences, 2008
- An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappingsJournal of Computational and Applied Mathematics, 2008
- A new iterative method for variational inequalitiesApplied Mathematics and Computation, 2006
- Picard iteration converges faster than Mann iteration for a class of quasi-contractive operatorsFixed Point Theory and Applications, 2004
- Fixed points by a new iteration methodProceedings of the American Mathematical Society, 1974
- Mean value methods in iterationProceedings of the American Mathematical Society, 1953