{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T22:27:32Z","timestamp":1785882452201,"version":"3.56.0"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,14]],"date-time":"2019-01-14T00:00:00Z","timestamp":1547424000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universiti Kebangsaan Malaysia  and Ministry of Education, Malaysia","award":["GP-K005224;   FRGS\/1\/2017\/STG06\/UKM\/01\/1"],"award-info":[{"award-number":["GP-K005224;   FRGS\/1\/2017\/STG06\/UKM\/01\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we initiate the notion of generalized multivalued     (  \u03b1  K  *  , \u03a5 , \u039b )    -contractions and provide some new common fixed point results in the class of     \u03b1 K    -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.<\/jats:p>","DOI":"10.3390\/sym11010086","type":"journal-article","created":{"date-parts":[[2019,1,14]],"date-time":"2019-01-14T12:20:07Z","timestamp":1547468407000},"page":"86","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":72,"title":["Hybrid Multivalued Type Contraction Mappings in \u03b1K-Complete Partial b-Metric Spaces and Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Eskandar","family":"Ameer","sequence":"first","affiliation":[{"name":"Department of Mathematics, Taiz University, Taiz, Yemen"},{"name":"Department of Mathematics, International Islamic University, H-10, Islamabad 44000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0003-3896-3809","authenticated-orcid":false,"given":"Hassen","family":"Aydi","sequence":"additional","affiliation":[{"name":"Imam Abdulrahman Bin Faisal University, Department of Mathematics, College of Education in Jubail, P.O. 12020, Industrial Jubail 31961, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Arshad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, International Islamic University, H-10, Islamabad 44000, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Habes","family":"Alsamir","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohd Selmi","family":"Noorani","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les operations dans les ensembles abstraits et leur application aux equations itegrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. 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