{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:38:36Z","timestamp":1740155916012,"version":"3.37.3"},"reference-count":12,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001332","name":"Council for Scientific and Industrial Research","doi-asserted-by":"publisher","award":["25 (0163)\/08\/EMR-II"],"award-info":[{"award-number":["25 (0163)\/08\/EMR-II"]}],"id":[{"id":"10.13039\/501100001332","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Operations Research"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>We introduce the notion of relaxed (\u03c1-\u03b8)-\u03b7-invariant pseudomonotone mappings, which is weaker than invariant pseudomonotone maps. Using the KKM technique, we establish the existence of solutions for variational-like inequality problems with relaxed (\u03c1-\u03b8)-\u03b7-invariant pseudomonotone mappings in reflexive Banach spaces. We also introduce the concept of (\u03c1-\u03b8)-pseudomonotonicity for bifunctions, and we consider some examples to show that (\u03c1-\u03b8)-pseudomonotonicity generalizes both monotonicity and strong pseudomonotonicity. The existence of solution for equilibrium problem with (\u03c1-\u03b8)-pseudomonotone mappings in reflexive Banach spaces are demonstrated by using the KKM technique.<\/jats:p>","DOI":"10.1155\/2012\/648070","type":"journal-article","created":{"date-parts":[[2012,1,19]],"date-time":"2012-01-19T16:04:01Z","timestamp":1326989041000},"page":"1-15","source":"Crossref","is-referenced-by-count":2,"title":["Variational-Like Inequalities and Equilibrium Problems with Generalized Monotonicity in Banach Spaces"],"prefix":"10.1155","volume":"2012","author":[{"given":"N. K.","family":"Mahato","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Nahak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2005.07.010"},{"issue":"1\u20134","key":"10","first-page":"123","volume":"63","year":"1994","journal-title":"The Mathematics Student"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025499305742"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-9659(99)00050-6"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7278"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02192248"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2007.02.004"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023953823177"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1998.6245"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2006.09.013"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01458545"},{"year":"1983","series-title":"Collection Math\u00e9matiques Appliqu\u00e9es pour la Ma\u00eetrise","key":"11"}],"container-title":["Advances in Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2012\/648070.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2012\/648070.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2012\/648070.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,2]],"date-time":"2016-08-02T18:05:26Z","timestamp":1470161126000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aor\/2012\/648070\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":12,"alternative-id":["648070","648070"],"URL":"https:\/\/doi.org\/10.1155\/2012\/648070","relation":{},"ISSN":["1687-9147","1687-9155"],"issn-type":[{"type":"print","value":"1687-9147"},{"type":"electronic","value":"1687-9155"}],"subject":[],"published":{"date-parts":[[2012]]}}}