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On different results for new three step iteration process in Banach spaces
Kifayat Ullah1, Muhammad Arshad1
1Department of Mathematics, International Islamic University, Sector H-10, Islamabad, 44000 Pakistan.
Springerplus
|September 22, 2016
Summary
A new AK iteration process approximates fixed points for contraction mappings more efficiently than the Vatan Two-step method. This study details the AK process
Area of Science:
- Numerical analysis
- Fixed-point theory
Background:
- Contraction mappings are fundamental in analysis.
- Approximating fixed points is crucial for solving equations.
- Existing iteration methods have limitations.
Purpose of the Study:
- Introduce a novel iteration process, the AK iteration process.
- Evaluate its efficiency for approximating fixed points of contraction mappings.
- Compare its performance against the Vatan Two-step iteration process.
Main Methods:
- Development of the AK iteration process algorithm.
- Analytical proofs demonstrating convergence and speed.
- Comparative analysis with the Vatan Two-step iteration process.
- Numerical examples to validate theoretical findings.
Main Results:
- The AK iteration process demonstrates faster convergence than the Vatan Two-step iteration process.
- Analytical proofs support the superiority of the AK iteration process.
- Numerical results confirm the enhanced performance and stability.
Conclusions:
- The AK iteration process is a more efficient method for fixed-point approximation.
- This new method offers advantages in speed and stability for contraction mappings.
- Further research can explore its application in broader mathematical contexts.
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