{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:22:00Z","timestamp":1760228520792,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T00:00:00Z","timestamp":1652745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Mianyang Teachers\u2019 College","award":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"],"award-info":[{"award-number":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"]}]},{"name":"National Natural Science Foundation of China","award":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"],"award-info":[{"award-number":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"]}]},{"name":"Central Government Funds of Guiding Local Scientific and Technological Development for Sichuan Province","award":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"],"award-info":[{"award-number":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"]}]},{"name":"Zigong Science and Technology Program","award":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"],"award-info":[{"award-number":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"]}]},{"name":"Opening Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things","award":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"],"award-info":[{"award-number":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"]}]},{"name":"2020 Graduate Innovation Project of Sichuan University of Science and Engineering","award":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"],"award-info":[{"award-number":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"]}]},{"name":"2021 Innovation and Entrepreneurship Training Program for College Students of Sichuan University of Science and Engineering","award":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"],"award-info":[{"award-number":["QD2019A08","11872043","2021ZYD0017","2020YGJC03","2020WYJ01","y2020078","cx2021150"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce some new types of extended Geraghty contractions, called (\u03b1,\u03b2)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty F-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.<\/jats:p>","DOI":"10.3390\/sym14051016","type":"journal-article","created":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T04:04:19Z","timestamp":1652760259000},"page":"1016","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fixed Point of (\u03b1,\u03b2)-Admissible Generalized Geraghty F-Contraction with Application"],"prefix":"10.3390","volume":"14","author":[{"given":"Min","family":"Wang","sequence":"first","affiliation":[{"name":"School of Science and Physics, Mianyang Teachers\u2019 College, Mianyang 621000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1485-6163","authenticated-orcid":false,"given":"Naeem","family":"Saleem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8904-6782","authenticated-orcid":false,"given":"Xiaolan","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"},{"name":"Key Laboratory of Higher Education of Sichuan Province for Enterprise, Informationlization and Internet of Things, Zigong 643000, China"},{"name":"South Sichuan Center for Applied Mathematics, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5527-1284","authenticated-orcid":false,"given":"Arslan Hojat","family":"Ansari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Karaj Brancem Islamic Azad University, Karaj 61349-37333, Iran"},{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University,  Pretoria 0204, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6496-4824","authenticated-orcid":false,"given":"Mi","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Science and Technology, Sanya University, Sanya 572000, China"},{"name":"Center for Mathematical Research, University of Sanya, Sanya 572022, China"},{"name":"Academician Guoliang Chen Team Innovation Center, University of Sanya, Sanya 572022, China"},{"name":"Academician Chunming Rong Workstation, University of Sanya, Sanya 572022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les oprationes dans les ensembles abstraits et leur application aux quation integrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1090\/S0002-9939-1973-0334176-5","article-title":"On contractive mappings","volume":"40","author":"Geraghty","year":"1973","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1186\/1687-1812-2012-74","article-title":"A generalization of Geraghtys theorem in partially ordered metric spaces and applications to ordinary differential equations","volume":"2012","author":"Gordji","year":"2012","journal-title":"Fixed Point Theory Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1186\/s13663-015-0426-y","article-title":"Common fixed point theorems for Geraghtys type contraction mappings using the monotone property with two metrics","volume":"2015","author":"Sintunavarat","year":"2015","journal-title":"Fixed Point Theory Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1186\/1687-1812-2013-180","article-title":"Best proximity points for Geraghtys proximal contraction mappings","volume":"2013","author":"Mongkolkehai","year":"2013","journal-title":"Fixed Point Theory Appl."},{"key":"ref_6","first-page":"26","article-title":"The contraction mapping principle in quasi metric spaces","volume":"30","author":"Bakhtin","year":"1989","journal-title":"Funct. Anal. Gos. Ped. Inst. Ulianowsk"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"941","DOI":"10.2478\/s12175-014-0250-6","article-title":"Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces","volume":"64","author":"Aghajani","year":"2014","journal-title":"Math. Slovaca"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s11784-018-0577-7","article-title":"Remarks on some fixed point results in b-metric space","volume":"20","author":"Huang","year":"2018","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"177","DOI":"10.24193\/fpt-ro.2019.1.10","article-title":"A fixed point theorem in uniform spaces generated by a family of b-pseudometrics","volume":"20","author":"Faraji","year":"2019","journal-title":"Fixed Point Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1007\/s13398-018-0524-x","article-title":"A common fixed point theorem of Fisher in b-metric spaces","volume":"113","author":"Hussain","year":"2019","journal-title":"Rev. R. Acad. Cienc. Exactas F\u00eds. Nat. Ser. A Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1007\/s11784-016-0400-2","article-title":"New fixed point theorems for set-valued contractions in b-metric spaces","volume":"19","author":"Miculsecu","year":"2017","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/s11784-019-0663-5","article-title":"A note on the results of Suzuki, Miculescu and Mihail","volume":"21","year":"2019","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1515\/ms-2017-0217","article-title":"Common fixed point theorems for a class of (s, q)-contractive mappings in b-metric-like spaces and applications to integral equations","volume":"69","author":"Zoto","year":"2019","journal-title":"Math. Slovaca"},{"key":"ref_14","first-page":"29","article-title":"On weak quasicontractions in b-metric spaces","volume":"94","author":"Hussain","year":"2019","journal-title":"Publ. Math. Debrecen"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1111\/j.1749-6632.1994.tb44144.x","article-title":"Partial metric topology, in Proceeding of the 8th summer conference on General Topology and Application","volume":"728","author":"Matthews","year":"1994","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1007\/s00009-013-0327-4","article-title":"Partial b-metric spaces and fixed point theorems","volume":"11","author":"Shukla","year":"2014","journal-title":"Mediterr. J. Math."},{"key":"ref_17","first-page":"562","article-title":"Some common fixed point results in ordered partial b-metric spaces","volume":"1","author":"Mustafa","year":"2014","journal-title":"J. Inequal. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2154","DOI":"10.1016\/j.na.2011.10.014","article-title":"Fixed point theorems for \u03b1- \u03c8-contractive type mappings","volume":"75","author":"Samet","year":"2012","journal-title":"Nonlinear Anal."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/1687-1812-2013-19","article-title":"Meir-Keeler \u03b1-contractive fixed and common fixed point theorems","volume":"2013","author":"Abdeljawad","year":"2013","journal-title":"Fixed Point Theory Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1186\/1687-1812-2013-329","article-title":"Fixed point theorems for \u03b1-Geraghty contraction type maps in metric spaces","volume":"2013","author":"Cho","year":"2013","journal-title":"Fixed Point Theory Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s40096-015-0159-4","article-title":"Some fixed point theorems for (\u03b1,\u03b2)-admissible geraghty type contractive mappings and related results","volume":"9","author":"Chandok","year":"2015","journal-title":"Math. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1186\/1687-1812-2012-94","article-title":"Fixed points of a new type of contractive mappings in complete metric spaces","volume":"1","author":"Wardowski","year":"2012","journal-title":"Fixed Point Theory Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1186\/1687-1812-2013-277","article-title":"Iterated function system consisting of F-contractions","volume":"1","author":"Secelean","year":"2013","journal-title":"Fixed Point Theory Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s00025-016-0570-7","article-title":"\u03c8F-contractions: Not necessarily nonexspansive Picard operators","volume":"70","author":"Secelean","year":"2016","journal-title":"Results Math."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1186\/1687-1812-2014-210","article-title":"Some fixed point theorems concerning F-contraction in complete metric spaces","volume":"1","author":"Piri","year":"2014","journal-title":"Fixed Point Theory Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"321","DOI":"10.24193\/fpt-ro.2018.1.25","article-title":"Fixed point results for various type F-contractions in complete b-metric spaces","volume":"19","year":"2018","journal-title":"Fixed Point Theory"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"969726","DOI":"10.1155\/2015\/969726","article-title":"Fixed points of generalized F-Suzuki type contraction in complete b-metric spaces","volume":"2015","author":"Alsulami","year":"2015","journal-title":"Discrete Dyn. Nat. Soc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"274","DOI":"10.15388\/NA.2016.2.9","article-title":"Fuzzy fixed points of generalized F2-Geraghty type fuzzy mappings and complementary results","volume":"21","author":"Abbas","year":"2016","journal-title":"Nonlinear Anal. Model. Control"},{"key":"ref_29","first-page":"5","article-title":"Contraction mappings in b-metric spaces","volume":"1","author":"Czerwik","year":"1993","journal-title":"Acta Math. Inform. Univ. Ostrav."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1016\/j.na.2010.09.025","article-title":"Equivalent conditions for generalized contractions on (ordered) metric spaces","volume":"74","author":"Jachymski","year":"2011","journal-title":"Nonlinear Anal."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Karapinar, E. (2019). Recent Advances on the Results for Nonunique Fixed in Various Spaces. Axioms, 8.","DOI":"10.3390\/axioms8020072"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"020048","DOI":"10.1063\/1.5020497","article-title":"Some fixed-circle theorems and discontinuity at fixed circle","volume":"1926","year":"2018","journal-title":"AIP Conf. Proc."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1007\/s40840-017-0555-z","article-title":"Some fixed-circle theorems on metric spaces","volume":"42","year":"2019","journal-title":"Bull. Malays. Math. Sci. Soc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/1016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:11:32Z","timestamp":1760137892000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/1016"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,17]]},"references-count":33,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14051016"],"URL":"https:\/\/doi.org\/10.3390\/sym14051016","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,5,17]]}}}