{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T22:01:02Z","timestamp":1773007262593,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T00:00:00Z","timestamp":1663632000000},"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 study, inspired by the concept of B-metric-like space (BMLS), we introduce the concept of orthogonal B-metric-like space (OBMLS) via a hybrid pair of operators. Additionally, we establish the concept of orthogonal dynamic system (ODS) as a generalization of the dynamic system (DS), which improves the existing results for analysies such as those presented here. By applying this, some new refinements of the F\u22a5-Suzuki-type (F\u22a5-ST) fixed-point results are presented. These include some tangible instances, and applications in the field of nonlinear analysis are given to highlight the usability and validity of the theoretical results.<\/jats:p>","DOI":"10.3390\/sym14101954","type":"journal-article","created":{"date-parts":[[2022,9,21]],"date-time":"2022-09-21T00:08:09Z","timestamp":1663718889000},"page":"1954","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Certain New Development to the Orthogonal Binary Relations"],"prefix":"10.3390","volume":"14","author":[{"given":"Amjad","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematics & Statistics, International Islamic University, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7742-5993","authenticated-orcid":false,"given":"Aftab","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-328X","authenticated-orcid":false,"given":"Muhammad","family":"Arshad","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, International Islamic University, Islamabad 44000, Pakistan"}]},{"given":"Hamed","family":"Al Sulami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"given":"Muhammad","family":"Tariq","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, International Islamic University, Islamabad 44000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Arshad, M., Abbas, M., Hussain, A., and Hussain, N. (2016). Generalized Dynamic Process for Generalized (f,L)-almost F-Contraction with Applications. J. Nonlinear Sci. 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Mathematics, 7.","DOI":"10.3390\/math7020132"},{"key":"ref_12","first-page":"143686","article-title":"Suzuki type fixed point results in metric-like spaces","volume":"2013","author":"Shobkolaei","year":"2013","journal-title":"J. Function Spaces Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5313","DOI":"10.1016\/j.na.2009.04.017","article-title":"A new type of fixed point theorem in metric spaces","volume":"71","author":"Suzuki","year":"2009","journal-title":"Nonlinear Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.na.2011.10.014","article-title":"Fixed point theorem for \u03b1-\u03c8-contractive type mappings","volume":"75","author":"Samet","year":"2012","journal-title":"Nonlinear Anal."},{"key":"ref_15","unstructured":"Srivastava, H.M., Ali, A., Hussain, A., Arshad, M., and Al-Sulami, H. (2022). A certain class of \u03b8L-type non-linear operatorsand some related fixed point results. J. Nonlinear Var. 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Fixed Point Theory Appl., 20.","DOI":"10.1007\/s11784-018-0510-0"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/1954\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:34:50Z","timestamp":1760142890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/1954"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,20]]},"references-count":32,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["sym14101954"],"URL":"https:\/\/doi.org\/10.3390\/sym14101954","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,20]]}}}