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Hierarchical fixed points of strictly pseudo contractive mappings for variational inequality problems
Tanom Chamnarnpan1, Nopparat Wairojjana, Poom Kumam
1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140 Thailand.
Springerplus
|November 21, 2013
Summary
This study presents a novel iterative method for finding common fixed points of strictly pseudo-contractive mappings in Hilbert spaces. The method also solves variational inequality problems linked to quadratic minimization.
Area of Science:
- Optimization Theory
- Functional Analysis
- Numerical Analysis
Background:
- Fixed-point theory is crucial for solving various mathematical problems.
- Variational inequality problems have applications in optimization and economics.
- Strictly pseudo-contractive mappings are a significant class of nonlinear operators.
Purpose of the Study:
- To develop a new iterative scheme for finding common fixed points.
- To ensure the convergence of the scheme to a solution of a variational inequality problem.
- To extend existing results in fixed-point theory and variational inequalities.
Main Methods:
- An iterative scheme is proposed and analyzed.
- Convergence analysis is performed in a real Hilbert space.
- The scheme is shown to converge strongly to a common fixed point.
Main Results:
- The introduced iterative scheme converges strongly to a common fixed point.
- This common fixed point is also a solution to a variational inequality problem.
- The results generalize and extend previous findings by Yao et al. and Gu et al.
Conclusions:
- The new iterative scheme is effective for solving problems involving strictly pseudo-contractive mappings.
- The findings contribute to the understanding of fixed-point iterations and variational inequalities.
- This research offers a unified approach to address related problems in mathematical analysis.
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