An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems
In this paper, we introduce a modified form of the <i>G</i>-variational inequality problem, called the combination of <i>G</i>-variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element b...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/1/122 |
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| Summary: | In this paper, we introduce a modified form of the <i>G</i>-variational inequality problem, called the combination of <i>G</i>-variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element between the set of fixed points of a <i>G</i>-nonexpansive mapping and the solution set of the proposed <i>G</i>-variational inequality problem. Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. Additionally, we present the concept of the <i>G</i>-minimization problem, which diverges from the conventional minimization problem. Applying our main results, we demonstrate a strong convergence theorem for the <i>G</i>-minimization problem. Finally, we provide illustrative examples to validate and support our theoretical findings. |
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| ISSN: | 2227-7390 |