{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:52:23Z","timestamp":1747191143041,"version":"3.40.5"},"reference-count":25,"publisher":"Wiley","license":[{"start":{"date-parts":[[2023,12,4]],"date-time":"2023-12-04T00:00:00Z","timestamp":1701648000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2023,12,4]]},"abstract":"<jats:p>This research paper introduces a comprehensive study on fixed points in orthogonal fuzzy metric spaces. The primary objective is to establish the existence and uniqueness of fixed points for self-mappings satisfying implicit relation criteria in complete orthogonal fuzzy metric spaces. By doing so, our proven results extend and generalise well-known findings in the field of fixed-point theory. To demonstrate the significance of the established results, several related examples are provided, serving to support and validate the theoretical findings in orthogonal fuzzy metric spaces. The implications of these results are discussed, shedding light on their potential applications in various practical scenarios. In addition to theoretical advancements, the paper also demonstrates a practical application of our established results in solving integral equations. This application exemplifies the effectiveness and versatility of the proposed approach in real-world problem-solving scenarios.<\/jats:p>","DOI":"10.1155\/2023\/5037401","type":"journal-article","created":{"date-parts":[[2023,12,4]],"date-time":"2023-12-04T17:35:09Z","timestamp":1701711309000},"page":"1-8","source":"Crossref","is-referenced-by-count":2,"title":["Fixed-Point Results for Mappings Satisfying Implicit Relation in Orthogonal Fuzzy Metric Spaces"],"prefix":"10.1155","volume":"2023","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7030-542X","authenticated-orcid":true,"family":"Sonam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Amity Institute of Applied Sciences, Amity University Kolkata, Kadampukur, West Bengal-700135, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0788-0760","authenticated-orcid":true,"given":"Vandana","family":"Rathore","sequence":"additional","affiliation":[{"name":"School of Engineering and Technology, Jagran Lakecity University, Bhopal, Madhya Pradesh-462044, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-8758-3821","authenticated-orcid":true,"given":"Amita","family":"Pal","sequence":"additional","affiliation":[{"name":"Marathwada Mitramandal\u2019s Institute of Technology, Lohegaon, Pune-411047, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1538-5615","authenticated-orcid":true,"given":"Ramakant","family":"Bhardwaj","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amity Institute of Applied Sciences, Amity University Kolkata, Kadampukur, West Bengal-700135, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9162-6310","authenticated-orcid":true,"given":"Satyendra","family":"Narayan","sequence":"additional","affiliation":[{"name":"Department of Applied Computing, Sheridan Institute of Technology, Oakville, ON L6H 2L1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/s0019-9958(65)90241-x"},{"issue":"5","key":"2","first-page":"336","article-title":"Fuzzy metrics and statistical metric spaces","volume":"11","author":"I. 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