{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:29:44Z","timestamp":1760149784997,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T00:00:00Z","timestamp":1693180800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"2020 Shanghai Leading Talents Program of the Shanghai Municipal Human Resources and Social Security Bureau","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]},{"name":"Innovation Program of Shanghai Municipal Education Commission","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]},{"name":"Program for Outstanding Academic Leaders in Shanghai City","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we design two inertial-type subgradient extragradient algorithms with the linear-search process for resolving the two pseudomonotone variational inequality problems (VIPs) of and the common fixed point problem (CFPP) of finite Bregman relatively nonexpansive operators and Bregman relatively demicontractive operators in Banach spaces of both p-uniform convexity and uniform smoothness, which are more general than Hilbert ones. By the aid of suitable restrictions, it is shown that the sequences fabricated by the suggested schemes converge weakly and strongly to a solution of a pair of VIPs with a CFPP constraint, respectively. Additionally, the illustrative instance is furnished to back up the practicability and implementability of the suggested methods. This paper reveals the competitive advantage of the proposed algorithms over the existing algorithms; that is, the existing hybrid projection method for a single VIP with an FPP constraint is extended to develop the modified inertial-type subgradient extragradient method for a pair of VIPs with an CFPP constraint.<\/jats:p>","DOI":"10.3390\/axioms12090832","type":"journal-article","created":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T08:59:05Z","timestamp":1693299545000},"page":"832","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modified Inertial-Type Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Finite Bregman Relatively Nonexpansive and Demicontractive Mappings"],"prefix":"10.3390","volume":"12","author":[{"given":"Cong-Shan","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3730-1475","authenticated-orcid":false,"given":"Lu-Chuan","family":"Ceng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sheng-Long","family":"Cao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui-Ying","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun-Shui","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1080\/02331934.2010.527340","article-title":"Hybrid extragradient methods for asymptotically strict pseudo-contractions in the intermediate sense and variational inequality problems","volume":"60","author":"Huang","year":"2011","journal-title":"Optimization"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1007\/s10898-018-0667-5","article-title":"A class of differential hemivariational inequalities in Banach spaces","volume":"72","author":"Zeng","year":"2018","journal-title":"J. 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