{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T23:05:35Z","timestamp":1777676735440,"version":"3.51.4"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,21]],"date-time":"2023-01-21T00:00:00Z","timestamp":1674259200000},"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>The notion of symmetry is the main property of a metric function. The area of fixed point theory has a suitable structure for symmetry in mathematics. The goal of this paper is to find fixed point and common fixed point results in a bicomplex valued b-metric space for mixed type rational contractions with control functions. Some well-known literature findings were generalized in our main findings. We provide an example to strengthen and validate our main results. As an example, in the context of bicomplex-valued b-metric space, we develop fixed point and common fixed point results for the rational contraction mapping.<\/jats:p>","DOI":"10.3390\/sym15020297","type":"journal-article","created":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T03:21:54Z","timestamp":1674616914000},"page":"297","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Solution of Fredholm Integral Equation via Common Fixed Point Theorem on Bicomplex Valued B-Metric Space"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4191-3338","authenticated-orcid":false,"given":"Gunaseelan","family":"Mani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6346-605X","authenticated-orcid":false,"given":"Arul Joseph","family":"Gnanaprakasam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Kanchipuram 603203, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3877-2714","authenticated-orcid":false,"given":"Ozgur","family":"Ege","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, Bornova, 35100 Izmir, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1511-9760","authenticated-orcid":false,"given":"Nahid","family":"Fatima","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"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":[[2023,1,21]]},"reference":[{"key":"ref_1","first-page":"26","article-title":"The Contraction Mapping Principle in Almost Metric Spaces","volume":"30","author":"Bakhtin","year":"1989","journal-title":"Funct. 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