{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:38:09Z","timestamp":1777703889971,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:00:00Z","timestamp":1565136000000},"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 & Fuzzy Systems"],"published-print":{"date-parts":[[2019,10,25]]},"abstract":"\n \u00a0In this paper, we introduce a new class of fuzzy contractive mappings under the name of \u2018\n \n \n (<\/mml:mo>\n F<\/mml:mi>\n Z<\/mml:mi>\n ,<\/mml:mo>\n \n F<\/mml:mi>\n ,<\/mml:mo>\n \u03c6<\/mml:mi>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:math>\n <\/jats:inline-formula>\n -contractive mappings\u2019 and utilize the same to prove fuzzy\n \u03c6<\/jats:italic>\n -fixed point results. Some illustrative examples are also given to support our results besides deriving several consequences. As an application, we prove an existence and uniqueness result on the solution of first order periodic differential equation. Interestingly, this newly introduced class unifies several known contractions such as: fuzzy contractive, fuzzy\n \u03c8<\/jats:italic>\n -contractive, fuzzy\n \n \n H<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n -contractive and fuzzy\n \n \n F<\/mml:mi>\n Z<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n -contractive mappings.\n <\/jats:p>","DOI":"10.3233\/jifs-190543","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T11:30:10Z","timestamp":1565695810000},"page":"5391-5402","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":19,"title":["New fuzzy\n \u03c6<\/i>\n -fixed point results employing a new class of fuzzy contractive mappings"],"prefix":"10.1177","volume":"37","author":[{"given":"Hayel N.","family":"Saleh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh, India"},{"name":"Department of Mathematics, Taiz University, Taiz, Yemen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Idrees A.","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Integral University, Lucknow, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad","family":"Imdad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Waleed M.","family":"Alfaqih","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hajjah University, Hajjah, Yemen"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,8,7]]},"reference":[{"issue":"5","key":"e_1_3_1_2_2","first-page":"141","article-title":"psi\u2013 weak contractions in fuzzy metric spaces","volume":"8","author":"Abbas M.","year":"2011","unstructured":"M.Abbas, M.Imdad and D.Gopal, psi\u2013 weak contractions in fuzzy metric spaces, Iranian Journal of Fuzzy Systems 8(5) (2011), 141\u2013148.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1155\/2010\/782680"},{"issue":"1","key":"e_1_3_1_4_2","first-page":"35","article-title":"Generalization of fixed point results for (\u03b1, \u03b7, \u03b2-contractive mappings in fuzzy metric spaces","volume":"3","author":"Babu G.","year":"2017","unstructured":"G.Babu, K.Sarma and Y.G.Aemro, Generalization of fixed point results for (\u03b1, \u03b7, \u03b2-contractive mappings in fuzzy metric spaces, Bangmod Int J Math & Comp Sci 3(1-2) (2017), 35\u201352.","journal-title":"Bangmod Int J Math & Comp Sci"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1969-0239559-9"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90162-7"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(88)90064-4"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.01.002"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00088-9"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","unstructured":"H.Jiang J.Zhan and D.Chen Covering based variable precision (I T)-fuzzy rough sets with applications to multi-attribute decision-making IEEE Transactions on Fuzzy Systems (2018). DOI: 10.1109\/TFUZZ.2018.2883023","DOI":"10.1109\/TFUZZ.2018.2883023"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1186\/1029-242X-2014-426"},{"issue":"5","key":"e_1_3_1_12_2","first-page":"336","article-title":"Fuzzy metrics and statistical metric spaces","volume":"11","author":"Kramosil I.","year":"1975","unstructured":"I.Kramosil and J.Mich\u00e1lek, Fuzzy metrics and statistical metric spaces, Kybernetika 11(5) (1975), 336\u2013344.","journal-title":"Kybernetika"},{"issue":"2","key":"e_1_3_1_13_2","first-page":"148","article-title":"Fixed point theorem using a new class of fuzzy contractive mappings","volume":"1","author":"Melliani S.","year":"2018","unstructured":"S.Melliani and A.Moussaoui, Fixed point theorem using a new class of fuzzy contractive mappings, Journal of Universal Mathematics 1(2) (2018), 148\u2013154.","journal-title":"Journal of Universal Mathematics"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2010.05.044"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.07.006"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-182873"},{"key":"e_1_3_1_17_2","first-page":"10","article-title":"A new method for some fixed point theorems in fuzzy metric spaces","volume":"3","author":"Sangurlu M.","year":"2017","unstructured":"M.Sangurlu, H.Isik and D.Turkoglu, A new method for some fixed point theorems in fuzzy metric spaces, Bangmod Int J Math & Comp Sci 3 (2017), 10\u201315.","journal-title":"Bangmod Int J Math & Comp Sci"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.22436\/jnsa.008.05.21"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1960.10.313"},{"issue":"2","key":"e_1_3_1_20_2","first-page":"137","article-title":"A new approach to caristi\u2019s fixed point theorem on non-archimedean fuzzy metric spaces","volume":"12","author":"Sedghi S.","year":"2015","unstructured":"S.Sedghi, N.Shobkolaei and I.Altun, A new approach to caristi\u2019s fixed point theorem on non-archimedean fuzzy metric spaces, Iranian Journal of Fuzzy Systems 12(2) (2015), 137\u2013143.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1515\/ms-2017-0115"},{"issue":"4","key":"e_1_3_1_22_2","article-title":"Some fixed point theorems of (F, \u03c6-fuzzy contractions in fuzzy metric spaces","volume":"8","author":"Sezen M.S.","year":"2017","unstructured":"M.S.Sezen and D.T\u00fcrko\u011flu, Some fixed point theorems of (F, \u03c6-fuzzy contractions in fuzzy metric spaces, Journal of Inequalities & Special Functions 8(4) (2017).","journal-title":"Journal of Inequalities & Special Functions"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-120721"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161467"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161919"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.01.012"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.10.016"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2019.01.004"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.11.033"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.04.054"}],"container-title":["Journal of Intelligent & Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-190543","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-190543","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-190543","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:54Z","timestamp":1777455594000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-190543"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,7]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,10,25]]}},"alternative-id":["10.3233\/JIFS-190543"],"URL":"https:\/\/doi.org\/10.3233\/jifs-190543","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,7]]}}}