{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T13:44:41Z","timestamp":1762782281475,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T00:00:00Z","timestamp":1549929600000},"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 article, we introduce and establish various approaches related to the F-contraction using new sorts of contractions, namely the extended     F  B e     -contraction, the extended     F  B e     -expanding contraction, and the extended generalized     F  B e     -contraction. Thereafter, we propose a simple and efficient solution for non-linear integral equations using the fixed point technique in the setting of a     B e    -metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples where necessary.<\/jats:p>","DOI":"10.3390\/sym11020206","type":"journal-article","created":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T02:49:44Z","timestamp":1550026184000},"page":"206","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["A New Approach to the Solution of Non-Linear Integral Equations via Various FBe-Contractions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0220-8222","authenticated-orcid":false,"given":"Sumati Kumari","family":"Panda","sequence":"first","affiliation":[{"name":"Department of Mathematics, Basic Sciences and Humanities, GMR Institute of Technology, Rajam 532127, Andhra Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6165-8055","authenticated-orcid":false,"given":"Asifa","family":"Tassaddiq","sequence":"additional","affiliation":[{"name":"College of Computer and Information Sciences, Majmaah University, Majmaah 11952, Saudi Arabia"}]},{"given":"Ravi P","family":"Agarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas A&amp;M University-Kingsville, Kingsville, TX 78363, USA"},{"name":"Distinguished University Professor of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/BF02421317","article-title":"Sur une classe d\u2019equations fonctionnelles","volume":"27","author":"Fredholm","year":"1903","journal-title":"Acta Math."},{"key":"ref_2","first-page":"369","article-title":"A note on the existaence of positive solution of Fredholm integral equations","volume":"5","author":"Rus","year":"2004","journal-title":"Fixed Point Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"735638","DOI":"10.1155\/2009\/735638","article-title":"Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation","volume":"2009","author":"Berenguer","year":"2009","journal-title":"Fixed Point Theory Appl."},{"key":"ref_4","first-page":"20187","article-title":"Fixed point theorems for (\u03b1,\u03d5) -contractive mappings of rational type in complex valued metric spaces with applications","volume":"2018","author":"Shahi","year":"2018","journal-title":"Results Fixed Point Theory Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s11784-018-0525-6","article-title":"Common fixed point results for new Ciric-type rational multivalued F-contraction with an application","volume":"20","author":"Rasham","year":"2018","journal-title":"J. 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Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1186\/s40064-015-1095-3","article-title":"d-Neighborhood system and generalized F-contraction in dislocated metric space","volume":"4","author":"Kumari","year":"2015","journal-title":"SpringerPlus"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1186\/s13663-016-0498-3","article-title":"Connecting various types of cyclic contractions and contractive self-mappings with Hardy-Rogers self-mappings","volume":"2016","author":"Kumari","year":"2016","journal-title":"Fixed Point Theory Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1186\/s13663-016-0521-8","article-title":"Cyclic compatible contraction and related fixed point theorems","volume":"2016","author":"Kumari","year":"2016","journal-title":"Fixed Point Theory Appl."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Sumati Kumari, P., Alqahtani, O., and Karap\u0131nar, E. (2018). Some Fixed-Point Theorems in b-Dislocated Metric Space and Applications. Symmetry, 10.","DOI":"10.3390\/sym10120691"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Kamran, T., Samreen, M., and Ain, Q.U. (2017). A generalization of b-metric space and some fixed point Theorems. Mathematics, 5.","DOI":"10.3390\/math5020019"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"15","DOI":"10.2298\/FIL1815337A","article-title":"On (\u03b1,\u03c8)-K-contractions in the extended b-metric space","volume":"32","author":"Alqahtani","year":"2018","journal-title":"Filomat"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Alqahtani, B., Fulga, A., and Karapinar, E. (2018). Non-Unique Fixed Point Results in Extended B-Metric Space. Mathematics, 6.","DOI":"10.3390\/math6050068"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1186\/s13660-018-1745-4","article-title":"Common fixed point results on extended b-metric space","volume":"2018","author":"Alqahtani","year":"2018","journal-title":"J. Inequal. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Karap\u0131nar, E., Kumari, P.S., and Lateef, D. (2018). A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces. Symmetry, 10.","DOI":"10.3390\/sym10100512"},{"key":"ref_19","first-page":"2018","article-title":"On New Fixed Point Results in Eb-Metric Spaces","volume":"16","author":"Kumari","year":"2018","journal-title":"Thai J. Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/206\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:31:30Z","timestamp":1760185890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,12]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["sym11020206"],"URL":"https:\/\/doi.org\/10.3390\/sym11020206","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,2,12]]}}}