{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T11:47:46Z","timestamp":1782733666973,"version":"3.54.5"},"reference-count":13,"publisher":"SAGE Publications","issue":"7","license":[{"start":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T00:00:00Z","timestamp":1765324800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems: Applications in Engineering and Technology"],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:p>This paper introduces the generalized fuzzy contraction in k-fuzzy metric spaces, a novel extension of the classical Meir-Keeler contraction principle. The main discovery is that several fixed point theorems, previously limited to classical or fuzzy metric spaces, remain valid under more general k-fuzzy conditions. This breakthrough broadens the applicability of fixed point theory to systems with multi-parameter uncertainty and non-uniform convergence, thereby offering a new mathematical tool for analyzing complex real-world problems in control theory, optimization, and data science.<\/jats:p>","DOI":"10.1177\/18758967251404855","type":"journal-article","created":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T16:54:39Z","timestamp":1765385679000},"page":"2101-2124","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["On k-Fuzzy Contraction Principles with Applications"],"prefix":"10.1177","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1274-1936","authenticated-orcid":false,"given":"Muhammad","family":"Nazam","sequence":"first","affiliation":[{"name":"Allama Iqbal Open University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-6287-5854","authenticated-orcid":false,"given":"Seemab","family":"Attique","sequence":"additional","affiliation":[{"name":"Allama Iqbal Open University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4833-753X","authenticated-orcid":false,"given":"Saud M","family":"Alsulami","sequence":"additional","affiliation":[{"name":"King Abdulaziz University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7742-5993","authenticated-orcid":false,"given":"Aftab","family":"Hussain","sequence":"additional","affiliation":[{"name":"King Abdulaziz University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2025,12,10]]},"reference":[{"key":"e_1_3_3_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-023-07946-y"},{"key":"e_1_3_3_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90162-7"},{"key":"e_1_3_3_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(88)90064-4"},{"issue":"2025","key":"e_1_3_3_5_1","first-page":"1","article-title":"Modified meir-keeler-type contraction in fuzzy metric spaces for single-valued and set-valued mappings with solution to boundary value problem","volume":"77","author":"Gupta V.","year":"2025","unstructured":"Gupta V., Dhawan P., Shukla R. (2025). Modified meir-keeler-type contraction in fuzzy metric spaces for single-valued and set-valued mappings with solution to boundary value problem. Boundary Value Problems, 77(2025), 1\u201323.\u00a0https:\/\/doi.org\/10.1186\/s13661-025-02065-z","journal-title":"Boundary Value Problems"},{"key":"e_1_3_3_6_1","first-page":"326","article-title":"Fuzzy metric and statistical metric spaces","volume":"15","author":"Kramosil I.","year":"1975","unstructured":"Kramosil I., Michalek J. (1975). Fuzzy metric and statistical metric spaces. Kybernetica, 15, 326\u2013334.","journal-title":"Kybernetica"},{"key":"e_1_3_3_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.07.006"},{"key":"e_1_3_3_8_1","doi-asserted-by":"publisher","DOI":"10.3390\/axioms13080558"},{"key":"e_1_3_3_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(90)90318-A"},{"key":"e_1_3_3_10_1","doi-asserted-by":"publisher","DOI":"10.2298\/FIL2014811R"},{"key":"e_1_3_3_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.01.012"},{"key":"e_1_3_3_12_1","doi-asserted-by":"publisher","DOI":"10.3390\/math11244962"},{"key":"e_1_3_3_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_3_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2018.08.014"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems: Applications in Engineering and Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/18758967251404855","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/18758967251404855","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/18758967251404855","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T11:34:30Z","timestamp":1782732870000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/18758967251404855"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,10]]},"references-count":13,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["10.1177\/18758967251404855"],"URL":"https:\/\/doi.org\/10.1177\/18758967251404855","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,10]]}}}