Two new iterative schemes to approximate the fixed points for mappings
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Aniruddha Deshmukh
Abstract
In this article, we present a study of two iterative schemes to approximate the fixed points of enriched non-expansive maps and enriched generalized non-expansive maps. The schemes introduced in this article generalize those given by Thakur et al. in (“A new iterative scheme for approximating fixed points of nonexpansive mappings,” Filomat, vol. 30, no. 10, pp. 2711–2720, 2016.) and Ali et al. in (“Approximation of Fixed points for Suzuki’s generalized nonexpansive mappings,” Mathematics, vol. 7, no. 6, pp. 522–532, 2019.) in a sense that our schemes work for larger classes of enriched mappings and the schemes given by Thakur et al. and Ali et al. reduce to a particular case of our iterative techniques. Taking inspiration from Berinde (“Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators,” Fixed Point Theory Appl., vol. 2004, no. 2, pp. 97–105, 2004.) and Maniu (“On a three-step iteration process for Suzuki mappings with qualitative study,” Numer. Funct. Anal. Optim., 2020.), we also give stability results of the our procedures for enriched contractions (introduced by Berinde in 2019). Lastly, we compare the rate of convergence of our schemes with each other and the conventional Krasnoselskii iteration process used for approximating fixed points of enriched contractions along with some examples. As an application to the proposed iterative schemes, we give a few results on the solutions of linear system of equations.
Acknowledgements
The authors thank Editor-in-Chief/Area Editors and Referee(s) for their valuable comments and suggestions, which were very much useful to improve the paper significantly.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Image-based 3D reconstruction precision using a camera mounted on a robot arm
- Switched-line network with digital phase shifter
- M-lump waves and their interactions with multi-soliton solutions for the (3 + 1)-dimensional Jimbo–Miwa equation
- Optimal control for a class of fractional order neutral evolution equations
- Perceptual evaluation for Zhangpu paper-cut patterns by using improved GWO-BP neural network
- Two new iterative schemes to approximate the fixed points for mappings
- Ulam’s type stability of impulsive delay integrodifferential equations in Banach spaces
- Generalization method of generating the continuous nested distributions
- Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay
- Numerical study of heat and mass transfer on the pulsatile flow of blood under atherosclerotic condition
- Dynamic propagation behaviors of pure mode I crack under stress wave loading by caustics
- Numerical simulation of buoyancy-induced heat transfer and entropy generation in 3D C-shaped cavity filled with CNT–Al2O3/water hybrid nanofluid
- On coupled system of nonlinear Ψ-Hilfer hybrid fractional differential equations
- Hellinger–Reissner variational principle for a class of specified stress problems
- Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition
- Fredholm determinants and Z n -mKdV/Z n -sinh-Gordon hierarchies
- New soliton waves and modulation instability analysis for a metamaterials model via the integration schemes
- A modified high-order symmetrical WENO scheme for hyperbolic conservation laws
- Cryptanalysis of various images based on neural networks with leakage and time varying delays
- Spectral collocation method approach to thermal stability of MHD reactive squeezed fluid flow through a channel
- Higher order Traub–Steffensen type methods and their convergence analysis in Banach spaces
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Image-based 3D reconstruction precision using a camera mounted on a robot arm
- Switched-line network with digital phase shifter
- M-lump waves and their interactions with multi-soliton solutions for the (3 + 1)-dimensional Jimbo–Miwa equation
- Optimal control for a class of fractional order neutral evolution equations
- Perceptual evaluation for Zhangpu paper-cut patterns by using improved GWO-BP neural network
- Two new iterative schemes to approximate the fixed points for mappings
- Ulam’s type stability of impulsive delay integrodifferential equations in Banach spaces
- Generalization method of generating the continuous nested distributions
- Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay
- Numerical study of heat and mass transfer on the pulsatile flow of blood under atherosclerotic condition
- Dynamic propagation behaviors of pure mode I crack under stress wave loading by caustics
- Numerical simulation of buoyancy-induced heat transfer and entropy generation in 3D C-shaped cavity filled with CNT–Al2O3/water hybrid nanofluid
- On coupled system of nonlinear Ψ-Hilfer hybrid fractional differential equations
- Hellinger–Reissner variational principle for a class of specified stress problems
- Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition
- Fredholm determinants and Z n -mKdV/Z n -sinh-Gordon hierarchies
- New soliton waves and modulation instability analysis for a metamaterials model via the integration schemes
- A modified high-order symmetrical WENO scheme for hyperbolic conservation laws
- Cryptanalysis of various images based on neural networks with leakage and time varying delays
- Spectral collocation method approach to thermal stability of MHD reactive squeezed fluid flow through a channel
- Higher order Traub–Steffensen type methods and their convergence analysis in Banach spaces
