{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:26:32Z","timestamp":1760149592738,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T00:00:00Z","timestamp":1693267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Arab Open University, Saudi Arabia","award":["AOURG-2023-006"],"award-info":[{"award-number":["AOURG-2023-006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>One of the frequently studied approaches in metric fixed-point theory is the generalization of the used metric space. Under this approach, in this study, we introduce a new extension of M-metric spaces, called controlled M-metric spaces, achieved by modifying the triangle inequality and keeping the symmetric condition of the space. The investigation focuses on exploring fundamental properties of this newly defined space, incorporating topological aspects. Several fixed-point theorems and fixed-circle results are established within these spaces complemented by illustrative examples to demonstrate the implications of our findings. Moreover, we present an application involving high-degree polynomial equations.<\/jats:p>","DOI":"10.3390\/sym15091665","type":"journal-article","created":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T08:26:52Z","timestamp":1693297612000},"page":"1665","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fixed Point Theorems in Symmetric Controlled M-Metric Type Spaces"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6530-5022","authenticated-orcid":false,"given":"Khaled","family":"Suwais","sequence":"first","affiliation":[{"name":"Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4535-4019","authenticated-orcid":false,"given":"Nihal","family":"Ta\u015f","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bal\u0131kesir University, Bal\u0131kesir 10145, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8152-1830","authenticated-orcid":false,"given":"Nihal","family":"\u00d6zg\u00fcr","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Izmir Democracy University, Karaba\u011flar, Izmir 35140, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Borisut, P., Kumam, P., Gupta, V., and Mani, N. (2019). Generalized (\u03c8,\u03b1,\u03b2)-weak Contractions for Initial Value Problems. Mathematics, 7.","DOI":"10.3390\/math7030266"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1007\/s11784-016-0303-2","article-title":"Fixed point theorems for (\u03c8,\u03b2)-Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations","volume":"19","author":"Gupta","year":"2017","journal-title":"J. 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Anal."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Mlaiki, N., Aydi, H., Souayah, N., and Abdeljawad, T. (2018). Controlled metric type spaces and the related contraction principle. Mathematics, 6.","DOI":"10.3390\/math6100194"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7008737","DOI":"10.1155\/2021\/7008737","article-title":"Double Controlled Partial Metric Type Spaces and Convergence Results","volume":"2021","author":"Ahmad","year":"2021","journal-title":"J. Math."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kamran, T., Samreen, M., and Ain, Q.U.L. (2017). A Generalization of b-metric space and some fixed point theorems. Mathematics, 5.","DOI":"10.3390\/math5020019"},{"key":"ref_10","first-page":"327","article-title":"A Banach type fixed point theorem","volume":"24","author":"Hicks","year":"1979","journal-title":"Math. Japan."},{"key":"ref_11","unstructured":"Ta\u015f, N., and \u00d6zg\u00fcr, N. (2022). Fixed Point Theory and Fractional Calculus-Recent Advances and Applications, Springer. Forum for Interdisciplinary Mathematics."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1080\/00029890.1999.12005131","article-title":"Descartes\u2019 rule of signs: Another construction","volume":"106","author":"Grabiner","year":"1999","journal-title":"Am. Math. Mon."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/9\/1665\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:41:46Z","timestamp":1760128906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/9\/1665"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,29]]},"references-count":12,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["sym15091665"],"URL":"https:\/\/doi.org\/10.3390\/sym15091665","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,8,29]]}}}