{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T15:49:27Z","timestamp":1725032967752},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T00:00:00Z","timestamp":1713657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"In this paper, we introduce the novel concept of generalized distance denoted as J\u03b8 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\u03b8(u,H\u2605), a generalized Hausdorff type distance and a PJ\u03b8-property of a pair (H\u2605,K\u2605) of nonempty subsets of extended b-metric space (U\u2605,\u03c1\u03b8). 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.<\/jats:p>","DOI":"10.3390\/sym16040502","type":"journal-article","created":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T11:44:09Z","timestamp":1713786249000},"page":"502","source":"Crossref","is-referenced-by-count":1,"title":["Best Proximity Point Results for Multi-Valued Mappings in Generalized Metric Structure"],"prefix":"10.3390","volume":"16","author":[{"given":"Asad Ullah","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}]},{"given":"Maria","family":"Samreen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-7742-5993","authenticated-orcid":false,"given":"Aftab","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5188-2830","authenticated-orcid":false,"given":"Hamed Al","family":"Sulami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,21]]},"reference":[{"key":"ref_1","first-page":"772","article-title":"La notion d\u2019\u00e9cart et le calcul fonctionnel","volume":"140","year":"1905","journal-title":"CR Acad. Sci. Paris"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"361","DOI":"10.2307\/2370790","article-title":"On semi-metric spaces","volume":"53","author":"Wilson","year":"1931","journal-title":"Am. J. Math."},{"key":"ref_3","first-page":"5","article-title":"Contraction mappings in b-metric spaces","volume":"1","author":"Czerwik","year":"1993","journal-title":"Acta Math. Inform. Univ. 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