{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:07:34Z","timestamp":1777367254447,"version":"3.51.4"},"reference-count":20,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T00:00:00Z","timestamp":1541030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we analyze two discontinuous self-mappings that satisfy Sehgal-type inequalities in the setup of complete b-metric space. The main results of the paper cover and extend a few existing results in the corresponding literature. Furthermore, we give some illustrative examples to verify the effectiveness and strength of our derived results. Thereafter, as an application, we consider the obtained result to aggregate the existence and uniqueness of the solution for nonlinear Fredholm integral equations.<\/jats:p>","DOI":"10.3390\/sym10110560","type":"journal-article","created":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T11:31:47Z","timestamp":1541071907000},"page":"560","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Sehgal Type Contractions on b-Metric Space"],"prefix":"10.3390","volume":"10","author":[{"given":"Badr","family":"Alqahtani","sequence":"first","affiliation":[{"name":"Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia"}]},{"given":"Andreea","family":"Fulga","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, Brasov 500036, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6798-3254","authenticated-orcid":false,"given":"Erdal","family":"Karap\u0131nar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey"},{"name":"Department of Medical Research, China Medical University, Taichung 40402, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1112\/jlms\/s2-5.3.571","article-title":"On fixed and periodic points for a class of mappings","volume":"5","author":"Sehgal","year":"1972","journal-title":"J. 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Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.22436\/jnsa.009.03.43","article-title":"Fixed point theorems for generalized (\u03b1-\u03c8)-\u0106iri\u0107-type contractive multivalued operators in b-metric spaces","volume":"9","author":"Bota","year":"2016","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_15","first-page":"1","article-title":"On some \u03b1-admissible contraction mappings on Branciari b-metric spaces","volume":"1","year":"2017","journal-title":"Adv. Theory Nonlinear Anal. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Karap\u0131nar, E., Piri, H., and Alsulami, H.H. (2015). Fixed points of generalized F-Suzuki type contraction in complete b-metric Spaces. Discret. Dyn. Nat. Soc., 2015.","DOI":"10.1186\/s13663-015-0377-3"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kutbi, M.A., Karap\u0131nar, E., Ahmed, J., and Azam, A. (2014). Some fixed point results for multi-valued mappings in b-metric spaces. J. Inequal. Appl., 2014.","DOI":"10.1186\/1029-242X-2014-126"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1515\/dema-2018-0019","article-title":"A short note on the common fixed points of the Geraghty contraction of type ES,T","volume":"51","author":"Alqahtani","year":"2018","journal-title":"Demonstr. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"517","DOI":"10.2140\/pjm.1977.71.517","article-title":"Fixed point theorems for mappings with a contractive iterate","volume":"71","author":"Ray","year":"1977","journal-title":"Pac. J. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1016\/j.jmaa.2016.02.053","article-title":"A remark on discontinuity at fixed point","volume":"445","author":"Bisht","year":"2017","journal-title":"J. Math. Anal. 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