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Approximation solution for system of generalized ordered variational inclusions with ⊕ operator in ordered Banach
Mohd Sarfaraz1, M K Ahmad1, A Kılıçman2
1Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Journal of Inequalities and Applications
|May 9, 2017
Summary
This study introduces a novel iterative algorithm for solving generalized ordered variational inclusions in real ordered Banach spaces. The research establishes an existence result and convergence criteria for the proposed algorithms.
Area of Science:
- Mathematical Analysis
- Optimization Theory
- Functional Analysis
Background:
- Variational inclusion problems are crucial in applied mathematics and optimization.
- Generalized ordered variational inclusions extend classical variational inequalities.
- Ordered Banach spaces provide a framework for studying inequalities and order structures.
Purpose of the Study:
- To investigate a system of generalized ordered variational inclusions with the ⊕ operator in a real ordered Banach space.
- To establish an existence result for the solution of this system.
- To develop and analyze a convergence scheme for iterative algorithms.
Main Methods:
- Application of the resolvent operator technique.
- Development of an iterative algorithm based on the resolvent operator.
- Analysis of convergence properties under specific conditions.
Main Results:
- An existence theorem for the solution of the generalized ordered variational inclusion system is proven.
- A convergence scheme for the iterative algorithms is established.
- The study discusses several special cases of the main problem.
Conclusions:
- The resolvent operator approach is effective for analyzing generalized ordered variational inclusions.
- The proposed iterative algorithm provides a method for approximating solutions.
- The findings contribute to the theory of variational inclusions and their applications.
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