{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T07:10:17Z","timestamp":1769843417708,"version":"3.49.0"},"reference-count":33,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T00:00:00Z","timestamp":1595203200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007613","name":"Majmaah University","doi-asserted-by":"publisher","award":["R-1441-137"],"award-info":[{"award-number":["R-1441-137"]}],"id":[{"id":"10.13039\/501100007613","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,7,20]]},"abstract":"<jats:p>Abdeljawad et al. (2018) introduced a new concept, named double controlled metric type spaces, as a generalization of the notion of extended <jats:italic>b<\/jats:italic>-metric spaces. In this paper, we extend their concept and introduce the concept of double controlled quasi-metric type spaces with two incomparable functions and prove some unique fixed point results involving new types of contraction conditions. Also, we introduce the concept of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>\u03b1<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mi>\u03bc<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mi>k<\/mml:mi><\/mml:math> double controlled contraction and prove some related fixed point results. We give several examples to show that our results are the proper generalization of the existing works.<\/jats:p>","DOI":"10.1155\/2020\/3460938","type":"journal-article","created":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T23:31:57Z","timestamp":1595287917000},"page":"1-8","source":"Crossref","is-referenced-by-count":8,"title":["Double Controlled Quasi-Metric Type Spaces and Some Results"],"prefix":"10.1155","volume":"2020","author":[{"given":"Abdullah","family":"Shoaib","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sabeena","family":"Kazi","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Humanities, College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6165-8055","authenticated-orcid":true,"given":"Asifa","family":"Tassaddiq","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Humanities, College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaif S.","family":"Alshoraify","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3712-072X","authenticated-orcid":true,"given":"Tahair","family":"Rasham","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.4064\/fm-3-1-133-181"},{"issue":"2","key":"2","first-page":"98","volume":"8","year":"2017","journal-title":"Journal of Mathematical Analysis"},{"issue":"4","key":"3","first-page":"692","volume":"24","year":"2018","journal-title":"Journal of Computational Analysis and Applications"},{"issue":"3","key":"4","first-page":"41","volume":"7","year":"2016","journal-title":"Journal of Mathematical Analysis"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.2307\/2371174"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/1812461"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.2298\/fil1711041a"},{"issue":"1","key":"8","first-page":"1","volume":"27","year":"2013","journal-title":"Fixed Point Theory Applications"},{"issue":"2","key":"9","volume":"16","year":"2015","journal-title":"Fixed Point Theory"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1186\/1029-242x-2014-36"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1109\/access.2019.2926798"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/603861"},{"issue":"5","key":"13","first-page":"975","volume":"25","year":"2018","journal-title":"Journal of Computational Analysis and Applications"},{"issue":"1","key":"14","first-page":"121","volume":"82","year":"2020","journal-title":"U.P.B. 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