{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:49:03Z","timestamp":1765212543226,"version":"3.46.0"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,30]],"date-time":"2025-11-30T00:00:00Z","timestamp":1764460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This study presents a common fixed-point iteration process that includes two asymptotically nonexpansive self-mappings in a hyperbolic space and their delta convergence. To support our results, we provide an example with a comparison table and sufficient conditions for a modified iteration scheme to have strong convergence to approximate the fixed point.<\/jats:p>","DOI":"10.3390\/axioms14120889","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:41:41Z","timestamp":1765212101000},"page":"889","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Common Fixed Point Approximation for Asymptotically Nonexpansive Mapping in Hyperbolic Space with Application"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-1595-2804","authenticated-orcid":false,"given":"Tehreem","family":"Ishtiaq","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi 46000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4729-4785","authenticated-orcid":false,"given":"Afshan","family":"Batool","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi 46000, 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, Jeddah, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5188-2830","authenticated-orcid":false,"given":"Hamed","family":"Alsulami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,30]]},"reference":[{"key":"ref_1","first-page":"794","article-title":"Un teorema generale sull\u2019esistenza di elementi uniti in una trasformazione funzionale","volume":"11","author":"Caccioppoli","year":"1930","journal-title":"Rend. 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