{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:28:40Z","timestamp":1772252920945,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T00:00:00Z","timestamp":1590796800000},"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, inspired by Jleli and Samet (Journal of Inequalities and Applications 38 (2014) 1\u20138), we introduce two new classes of auxiliary functions and utilize the same to define      ( \u03b8 , \u03c8 )  R    -weak contractions. Utilizing      ( \u03b8 , \u03c8 )  R    -weak contractions, we prove some fixed point theorems in the setting of relational metric spaces. We employ some examples to substantiate the utility of our newly proven results. Finally, we apply one of our newly proven results to ensure the existence and uniqueness of the solution of a Volterra-type integral equation.<\/jats:p>","DOI":"10.3390\/sym12060887","type":"journal-article","created":{"date-parts":[[2020,6,3]],"date-time":"2020-06-03T04:12:09Z","timestamp":1591157529000},"page":"887","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New Fixed Point Results via (\u03b8,\u03c8)R-Weak Contractions with an Application"],"prefix":"10.3390","volume":"12","author":[{"given":"Mohammad","family":"Imdad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Based","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6281-1229","authenticated-orcid":false,"given":"Waleed M.","family":"Alfaqih","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hajjah University, Hajjah 1729, Yemen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4303-2884","authenticated-orcid":false,"given":"Salvatore","family":"Sessa","sequence":"additional","affiliation":[{"name":"Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdullah","family":"Aldurayhim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Prince Sattam Bin Abdulaziz University, Alkharj 11911, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leur application aux \u00e9quations int\u00e9grales","volume":"1","author":"Banach","year":"1922","journal-title":"Fund. 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Ser."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1007\/s11784-015-0247-y","article-title":"Relation-theoretic contraction principle","volume":"4","author":"Alam","year":"2015","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_12","unstructured":"Lipschutz, S. (1976). Schaum\u2019s Outline of Theory and Problems of Set Theory and Related Topics, Tata McGraw-Hill."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4421","DOI":"10.2298\/FIL1714421A","article-title":"Relation-theoretic metrical coincidence theorems","volume":"14","author":"Alam","year":"2017","journal-title":"Filomat"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Berzig, M., Karap\u0131nar, E., and Rold\u00e1n-L\u00f3pez-de Hierro, A.-F. (2014). Discussion on generalized-(\u03b1\u03c8, \u03b2)-contractive mappings via generalized altering distance function and related fixed point theorems. Abstract and Applied Analysis, Hindawi Publishing Corporation.","DOI":"10.1155\/2014\/259768"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/887\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:34:04Z","timestamp":1760175244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/6\/887"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,30]]},"references-count":14,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["sym12060887"],"URL":"https:\/\/doi.org\/10.3390\/sym12060887","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202005.0046.v1","asserted-by":"object"}]},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,30]]}}}