An iterative algorithm for a system of generalized implicit variational inclusions
Iqbal Ahmad1, Vishnu Narayan Mishra2, Rais Ahmad1
1Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Springerplus
|August 23, 2016
Summary
This study introduces a new system of generalized implicit variational inclusions. An iterative algorithm is developed to approximate solutions, and its convergence is analyzed.
Area of Science:
- Optimization Theory
- Applied Mathematics
- Numerical Analysis
Background:
- Variational inclusion systems are crucial in applied mathematics.
- Existing methods may have limitations in solving complex systems.
- Generalized implicit variational inclusions present unique challenges.
Purpose of the Study:
- To introduce and analyze a system of generalized implicit variational inclusions.
- To develop an iterative algorithm for approximating solutions to this system.
- To investigate the convergence properties of the proposed algorithm.
Main Methods:
- Formulation of a system of three generalized implicit variational inclusions.
- Design of an iterative algorithm incorporating error terms.
- Application of a relaxed resolvent operator technique.
- Theoretical analysis of the convergence of iterative sequences.
Main Results:
- A novel system of generalized implicit variational inclusions is presented.
- An iterative algorithm is proposed for approximating solutions.
- The convergence of the iterative sequences generated by the algorithm is demonstrated.
- A supporting example validates the theoretical findings.
Conclusions:
- The proposed iterative algorithm effectively approximates solutions for the generalized implicit variational inclusion system.
- The convergence analysis provides theoretical guarantees for the algorithm's performance.
- This work contributes a new method for solving a class of complex mathematical problems.
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