BEST PROXIMITY POINTS FOR WEAK PROXIMAL ENRICHED <i>G</i>-CONTRACTIONS IN GRAPHICAL CONVEX METRIC SPACES

Chaobo Li; Yunan Cui; Rizwan Anjum

doi:10.11948/20240484

2025 Volume 15 Issue 4

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Chaobo Li, Yunan Cui, Rizwan Anjum. BEST PROXIMITY POINTS FOR WEAK PROXIMAL ENRICHED G-CONTRACTIONS IN GRAPHICAL CONVEX METRIC SPACES[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2392-2407. doi: 10.11948/20240484

Citation:

Chaobo Li, Yunan Cui, Rizwan Anjum. BEST PROXIMITY POINTS FOR WEAK PROXIMAL ENRICHED G-CONTRACTIONS IN GRAPHICAL CONVEX METRIC SPACES[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2392-2407. doi: 10.11948/20240484

BEST PROXIMITY POINTS FOR WEAK PROXIMAL ENRICHED G-CONTRACTIONS IN GRAPHICAL CONVEX METRIC SPACES

1.
Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
2.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan

Author Bio: Email: cuiya@hrbust.edu.cn(Y. Cui); Email: rizwan.anjum@ue.edu.pk(R. Anjum)
Corresponding author: Email: lichaobo6898@163.com(C. Li)

Abstract

Abstract

In this paper, we redefine the concept of a graphical convex metric space involving sets with a graphical structure, and a new class of non-self mappings, called weak proximal enriched $ G- $contractions, is introduced in the aforementioned space. Moreover, we demonstrate the existence of best approximation points for two types of weak proximal enriched $ G- $contractions in graphical convex metric spaces, under suitable control conditions. Additionally, we provide examples to confirm our main results.
- Graphical convex metric space /
- weak enriched G-contraction /
- best proximity point /
- directed graph
MSC: 47H09, 47H10

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References

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