{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:16:49Z","timestamp":1760059009546,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T00:00:00Z","timestamp":1747008000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2025"],"award-info":[{"award-number":["QU-APC-2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper is devoted to the analysis of a system of generalized variational inclusion problems involving \u03b1-averaged and Cayley operators within the framework of a q-uniformly smooth Banach space. We demonstrate that the problem can be reformulated as an equivalent fixed-point equation and propose an iterative method based on the fixed-point approach to obtain the solution. Furthermore, we establish the existence of solutions and analyze the convergence properties of the proposed algorithm under suitable conditions. To validate the effectiveness of the proposed iterative method, we provide a numerical result supported by a computational graph and a convergence plot, illustrating its performance and efficiency.<\/jats:p>","DOI":"10.3390\/axioms14050361","type":"journal-article","created":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T09:13:38Z","timestamp":1747041218000},"page":"361","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convergence Analysis for System of Cayley Generalized Variational Inclusion on q-Uniformly Banach Space"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-0619-0183","authenticated-orcid":false,"given":"Mohd Falahat","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4613-3269","authenticated-orcid":false,"given":"Syed Shakaib","family":"Irfan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8447-0709","authenticated-orcid":false,"given":"Iqbal","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, College of Engineering, Qassim University, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1080\/00036811.2020.1781822","article-title":"Cayley inclusion problem with its corresponding generalized resolvent equation problem in uniformly smooth Banach spaces","volume":"101","author":"Ahmad","year":"2022","journal-title":"Appl. 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Mathematics, 10.","DOI":"10.3390\/math10214131"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1007\/s12215-023-00988-z","article-title":"System of generalized nonlinear variational-like inclusions and fixed point problems: Graph convergence with an application","volume":"73","author":"Balooee","year":"2024","journal-title":"Rend. Circ. Mat. Palermo Ser. 2"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"549","DOI":"10.19139\/soic-2310-5070-884","article-title":"Iterative Algorithms for a Generalized System of Mixed Variational-Like Inclusion Problems and Altering Points Problem","volume":"8","author":"Alansari","year":"2020","journal-title":"Stat. Optim. Inf. Comput."},{"key":"ref_19","first-page":"309","article-title":"General bivariational inclusions and iterative methods","volume":"14","author":"Noor","year":"2023","journal-title":"Int. J. Nonlinear Anal. Appl."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/361\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:31:00Z","timestamp":1760031060000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/5\/361"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,12]]},"references-count":19,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["axioms14050361"],"URL":"https:\/\/doi.org\/10.3390\/axioms14050361","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,5,12]]}}}