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
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页数:23
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