{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T13:19:18Z","timestamp":1770297558322,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T00:00:00Z","timestamp":1748563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2025R45"],"award-info":[{"award-number":["PNURSP2025R45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This work develops and analyzes an iterative method to solve the combined generalized equilibrium and fixed point problems involving two relatively nonexpansive mappings. We establish that the generated sequence converges strongly to a shared solution within a two-uniformly convex and uniformly smooth real Banach space. We also highlight some immediate consequences of the main result. To confirm the algorithm\u2019s efficiency, a numerical example is provided. Furthermore, the practical utility of the proposed algorithm is illustrated using comprehensive tables and figures.<\/jats:p>","DOI":"10.3390\/axioms14060428","type":"journal-article","created":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T10:21:49Z","timestamp":1748859709000},"page":"428","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the Strong Convergence of Combined Generalized Equilibrium and Fixed Point Problems in a Banach Space"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2222-7973","authenticated-orcid":false,"given":"Ghada","family":"AlNemer","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3221-3698","authenticated-orcid":false,"given":"Rehan","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Central University of Kashmir Ganderbal, Jammu and Kashmir 191131, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9713-3509","authenticated-orcid":false,"given":"Mohammad","family":"Farid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1073\/pnas.54.4.1041","article-title":"Nonexpansive nonlinear operators in a Banach space","volume":"54","author":"Browder","year":"1965","journal-title":"Proc. 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