{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T07:28:09Z","timestamp":1769585289872,"version":"3.49.0"},"reference-count":18,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2024,1,10]]},"abstract":"<jats:p>In this article, the probabilistic metric distance between two disjoint sets is utilised to define the essential criteria for the existence and uniqueness of the best proximity point, which takes into account the global optimization problem. In order to solve this problem, we pretend that we are trying to obtain the optimal approximation to the solution of a fixed point equation. Here, we introduce two types of probabilistic proximal contraction mappings and use a geometric property called \u03a9-property in the context of probabilistic metric spaces. We also obtain some consequences for self-mappings, which give the fixed point results. Some examples are provided to validate the findings. As an application, we obtain the solution to a second-order boundary value problem using a minimum t-norm in the context of probabilistic metric spaces.<\/jats:p>","DOI":"10.3233\/jifs-231315","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T11:24:28Z","timestamp":1702380268000},"page":"2207-2218","source":"Crossref","is-referenced-by-count":0,"title":["Global optimization problem and probabilistic distance"],"prefix":"10.1177","volume":"46","author":[{"given":"Samir Kumar","family":"Bhandari","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bajkul Milani Mahavidyalaya, Bajkul, West Bengal, India"}]},{"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Department of Electricity and Electronics, Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, Spain"}]},{"given":"Sumit","family":"Chandok","sequence":"additional","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering and Technology, Deemed to be University, Patiala, Punjab, India"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-231315_ref1","doi-asserted-by":"crossref","first-page":"3790","DOI":"10.1016\/j.na.2007.10.014","article-title":"Best proximity points for cyclic Mier-Keeler contractions","volume":"69","author":"Bari","year":"2008","journal-title":"Nonlinear Anal"},{"key":"10.3233\/JIFS-231315_ref2","doi-asserted-by":"crossref","first-page":"257","DOI":"10.2298\/AADM120526012B","article-title":"Nonlinear generalized contraction on Menger PM-spaces","volume":"6","author":"Babacev","year":"2012","journal-title":"Appl Anal Discrete Math"},{"key":"10.3233\/JIFS-231315_ref3","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s10013-015-0141-3","article-title":"Best proximity point results in generalized metric spaces","volume":"44","author":"Choudhury","year":"2016","journal-title":"Vietnam J Math"},{"key":"10.3233\/JIFS-231315_ref4","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1016\/j.jmaa.2005.10.081","article-title":"Existence and convergence of best proximity points","volume":"323","author":"Eldred","year":"2006","journal-title":"J Math Anal Appl"},{"key":"10.3233\/JIFS-231315_ref5","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2022.2072219"},{"key":"10.3233\/JIFS-231315_ref7","doi-asserted-by":"crossref","first-page":"3177","DOI":"10.1007\/s11784-017-0479-0","article-title":"\u03a6-Best proximity point theorems and applications to variational inequality problem","volume":"19","author":"Isik","year":"2017","journal-title":"J Fixed point Theory Appl"},{"key":"10.3233\/JIFS-231315_ref8","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1016\/j.bulsci.2013.02.003","article-title":"Best proximity points for \u03b1 \u2013\u03c8-proximal contractive type mappings and applications","volume":"137","author":"Jleli","year":"2013","journal-title":"Bull Sci Math"},{"key":"10.3233\/JIFS-231315_ref9","doi-asserted-by":"crossref","unstructured":"Jleli M. , Karapinar E. and Samet B. , Best proximity point result for MK-proximal contractions, Abstr Appl Anal 2012 (2012). 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