{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T22:19:04Z","timestamp":1775168344407,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,6,30]],"date-time":"2024-06-30T00:00:00Z","timestamp":1719705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>By revisiting an open question raised by Kirk and Shahzad, we are able to prove a generalized version of Nadler\u2019s fixed-point theorem in the context of strong b-metric space. Such a result leads us to prove a new version of Dontchev and Hager\u2019s inverse mapping theorem. Some examples are provided to illustrate the results.<\/jats:p>","DOI":"10.3390\/axioms13070445","type":"journal-article","created":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T10:14:46Z","timestamp":1719828886000},"page":"445","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On a Version of Dontchev and Hager\u2019s Inverse Mapping Theorem"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5549-4912","authenticated-orcid":false,"given":"Thanaa A.","family":"Alarfaj","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"},{"name":"Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31441, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4833-753X","authenticated-orcid":false,"given":"Saud M.","family":"Alsulami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,30]]},"reference":[{"key":"ref_1","unstructured":"Bourbaki, N. (1974). Topologie G\u00e9n\u00e9rale (General Topology), Hermann."},{"key":"ref_2","first-page":"26","article-title":"The contraction mapping in almost metric spaces, Funct","volume":"30","author":"Bakhtin","year":"1989","journal-title":"Funct. Ana. Gos. Ped. Inst. Unianowsk"},{"key":"ref_3","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_4","first-page":"263","article-title":"Nonlinear set-valued contraction mappings in b-metric spaces","volume":"46","author":"Czerwik","year":"1998","journal-title":"Atti Sem. Mat. Fis. Univ. Modena"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.22436\/jnsa.008.06.11","article-title":"Rectangular b-metric space and contraction principles","volume":"8","author":"George","year":"2015","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kirk, W., and Shahzad, N. (2014). Fixed Point Theory in Distance Spaces, Springer.","DOI":"10.1007\/978-3-319-10927-5"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.11650\/tjm.20.2016.6359","article-title":"Answers to Kirk-Shahzad\u2019s Questions on Strong b-metric Spaces","volume":"20","author":"An","year":"2016","journal-title":"Taiwanese J. Math."},{"key":"ref_8","first-page":"3","article-title":"Generalized contractions in quasimetric spaces","volume":"3","author":"Berinde","year":"1993","journal-title":"Semin. Fixed Point Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/s11784-015-0273-9","article-title":"On relaxations of contraction constants and Caristi\u2019s theorem in b-metric spaces","volume":"18","author":"Dung","year":"2016","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"718074","DOI":"10.1155\/2015\/718074","article-title":"Fixed points for multivalued mappings in b-metric spaces","volume":"2015","author":"Jleli","year":"2015","journal-title":"Abstr. Appl. Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3123","DOI":"10.1016\/j.na.2010.06.084","article-title":"KKM mappings in metric type spaces","volume":"73","author":"Khamsi","year":"2010","journal-title":"Nonlinear Anal. 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Anal."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7895","DOI":"10.3934\/math.2021458","article-title":"A new type of Kannan\u2019s fixed point theorem in strong b-metric spaces","volume":"6","author":"Doan","year":"2021","journal-title":"Aims Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"289","DOI":"10.5486\/PMD.2019.8260","article-title":"On weak quasicontractions in b-metric spaces","volume":"94","author":"Mitrovic","year":"2019","journal-title":"Publ. Math. Debrecen"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1186\/s13660-022-02814-z","article-title":"Fixed points of single-valued and multi-valued mappings in sb-metric spaces","volume":"2022","author":"Tassaddiq","year":"2022","journal-title":"J. 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