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Mann iteration for monotone nonexpansive mappings in ordered CAT(0) space with an application to integral equations
Izhar Uddin1, Chanchal Garodia1, Juan Jose Nieto2
11Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi, India.
Journal of Inequalities and Applications
|March 7, 2019
Summary
This study proves convergence for monotone nonexpansive mappings in a specific space using the Mann iteration scheme. The findings are illustrated with a numerical example and applied to solve integral equations.
Area of Science:
- Nonlinear analysis
- Functional analysis
- Metric spaces
Background:
- Monotone nonexpansive mappings are crucial in various mathematical fields.
- Understanding their convergence properties is essential for solving equations.
- Existing iteration schemes have limitations in certain spaces.
Purpose of the Study:
- To establish convergence results for monotone nonexpansive mappings.
- To analyze the Mann iteration scheme in a specific space.
- To extend existing convergence theorems.
Main Methods:
- Utilizing the Mann iteration scheme.
- Proving both Δ-convergence and strong convergence.
- Developing a numerical example for validation.
Main Results:
- Demonstrated convergence of the Mann iteration scheme.
- Provided a numerical example confirming the theoretical results.
- Extended existing convergence results for monotone nonexpansive mappings.
Conclusions:
- The Mann iteration scheme effectively converges for monotone nonexpansive mappings in the studied space.
- The findings have implications for solving integral equations.
- This work contributes to the advancement of nonlinear analysis and iterative methods.
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