Best Proximity Point Results for Multi-Valued Mappings in Generalized Metric Structure

被引：2

作者：

Khan, Asad Ullah ^{[1
]}

Samreen, Maria ^{[1
]}

Hussain, Aftab ^{[2
]}

Al Sulami, Hamed ^{[2
]}

机构：

[1] Quaid I Azam Univ, Dept Math, Islamabad 45320, Pakistan

[2] King Abdulaziz Univ, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

来源：

SYMMETRY-BASEL | 2024年 / 16卷 / 04期

关键词：

best proximity point; fixed point; multi-valued contraction; b-metric; extended b-generalized pseudo-distance; FIXED-POINT; THEOREMS; SPACE; APPROXIMATION; CONTRACTIONS; CONVERGENCE;

D O I：

10.3390/sym16040502

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we introduce the novel concept of generalized distance denoted as J theta and call it an extended b-generalized pseudo-distance. With the help of this generalized distance, we define a generalized point to set distance J theta(u,H star), a generalized Hausdorff type distance and a PJ theta-property of a pair (H star,K star) of nonempty subsets of extended b-metric space (U star,rho theta). Additionally, we establish several best proximity point theorems for multi-valued contraction mappings of Nadler type defined on b-metric spaces and extended b-metric spaces. Our findings generalize numerous existing results found in the literature. To substantiate the introduced notion and validate our main results, we provide some concrete examples.

引用

页数：23

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