Hammerstein Nonlinear Integral Equations and Iterative Methods for the Computation of Common Fixed Points
Abstract
:1. Introduction
- is continuous in y for almost all x, and measurable in x for any fixed y,
- is nondecreasing for any fixed x,
- for any fixed y, and
- the linear integral operator associated with is bounded from into and positive,
2. Solution of a Type of Nonlinear Hammerstein Integral Equation
3. A Modified Algorithm for the Search of Common Fixed Points of Nearly Asymptotically Nonexpansive Mappings
- 1.
- the map N defined as is asymptotically regular, and,
- 2.
- if additionally is uniformly continuous, the sequence has the AF property with respect to .
4. An Iterative Method for the Search of Common Fixed Points of a Finite Number of Quasi-Nonexpansive Operators
- 1.
- The sequence has the CLE property for any
- 2.
- The sequence has the AF property with respect to for any
Strong Convergence of the m-Steps Common N-Iteration
5. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
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Iteration (n) | |
---|---|
1 | 0.216882 |
2 | 0.098364 |
3 | 0.043072 |
4 | 0.018419 |
5 | 0.007786 |
6 | 0.003275 |
7 | 0.001375 |
8 | 0.000577 |
9 | 0.000242 |
10 | 0.000103 |
Iteration (n) | |
---|---|
0 | 0.57735 |
1 | 0.056664 |
2 | 0.006714 |
3 | 0.000841 |
4 | 0.000108 |
5 | 0.000014 |
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Navascués, M.A. Hammerstein Nonlinear Integral Equations and Iterative Methods for the Computation of Common Fixed Points. Axioms 2025, 14, 214. https://doi.org/10.3390/axioms14030214
Navascués MA. Hammerstein Nonlinear Integral Equations and Iterative Methods for the Computation of Common Fixed Points. Axioms. 2025; 14(3):214. https://doi.org/10.3390/axioms14030214
Chicago/Turabian StyleNavascués, María A. 2025. "Hammerstein Nonlinear Integral Equations and Iterative Methods for the Computation of Common Fixed Points" Axioms 14, no. 3: 214. https://doi.org/10.3390/axioms14030214
APA StyleNavascués, M. A. (2025). Hammerstein Nonlinear Integral Equations and Iterative Methods for the Computation of Common Fixed Points. Axioms, 14(3), 214. https://doi.org/10.3390/axioms14030214