{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:37:51Z","timestamp":1753886271491,"version":"3.41.2"},"reference-count":28,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,5,30]],"date-time":"2012-05-30T00:00:00Z","timestamp":1338336000000},"content-version":"vor","delay-in-days":150,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71161001-G0105","11071279","20091003"],"award-info":[{"award-number":["71161001-G0105","11071279","20091003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71161001-G0105","11071279","20091003"],"award-info":[{"award-number":["71161001-G0105","11071279","20091003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Colleges and Universities Science and Technology Development Foundation","award":["71161001-G0105","11071279","20091003"],"award-info":[{"award-number":["71161001-G0105","11071279","20091003"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We use the auxiliary principle technique to suggest and analyze an implicit method for solving the equilibrium problems on Hadamard manifolds. The convergence of this new implicit method requires only the speudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered.<\/jats:p>","DOI":"10.1155\/2012\/437391","type":"journal-article","created":{"date-parts":[[2012,5,31]],"date-time":"2012-05-31T22:49:28Z","timestamp":1338504568000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Implicit Methods for Equilibrium Problems on Hadamard Manifolds"],"prefix":"10.1155","volume":"2012","author":[{"given":"Muhammad Aslam","family":"Noor","sequence":"first","affiliation":[]},{"given":"Saira","family":"Zainab","sequence":"additional","affiliation":[]},{"given":"Yonghong","family":"Yao","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,5,30]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2004.10.008"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.11.001"},{"key":"e_1_2_6_3_2","series-title":"Mathematics: Theory & Applications","volume-title":"Riemannian Geometry","author":"DoCarmo M. P.","year":"1992"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1080\/02331930290019413"},{"key":"e_1_2_6_5_2","unstructured":"NoorM. A.andNoorK. I. Proximal point methods for solving mixed variational inequalities on Hadamard manifolds Journal of Applied Mathematics. In press."},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/149"},{"key":"e_1_2_6_7_2","unstructured":"TangG. ZhouL. W. andHuangN. J. The proximal point algorithm for pseudomonotone variational inequalities on Hadamard manifolds Optimization Letters. In presshttps:\/\/doi.org\/10.1007\/s11590%2D012%2D0459%2D7."},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8390-9"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(02)00266-3"},{"key":"e_1_2_6_10_2","first-page":"313","article-title":"On general nonlinear complementarity problems and quasi-equilibria","volume":"49","author":"Noor M. A.","year":"1994","journal-title":"Le Matematiche"},{"key":"e_1_2_6_11_2","first-page":"123","article-title":"From optimization and variational inequalities to equilibrium problems","volume":"63","author":"Blum E.","year":"1994","journal-title":"The Mathematics Student"},{"key":"e_1_2_6_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-010-0169-1"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0893-9659(88)90054-7"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7042"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00558-7"},{"key":"e_1_2_6_16_2","first-page":"137","article-title":"Fundamentals of mixed quasi variational inequalities","volume":"15","author":"Noor M. A.","year":"2004","journal-title":"International Journal of Pure and Applied Mathematics"},{"key":"e_1_2_6_17_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTA.0000042526.24671.b2"},{"key":"e_1_2_6_18_2","doi-asserted-by":"publisher","DOI":"10.7153\/mia-09-51"},{"key":"e_1_2_6_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2008.03.007"},{"key":"e_1_2_6_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-010-9717-y"},{"key":"e_1_2_6_21_2","first-page":"89","article-title":"Auxiliary principle technique for solving general mixed variational inequalities","volume":"3","author":"Noor M. A.","year":"2010","journal-title":"Journal of Advanced Mathematical Studies"},{"key":"e_1_2_6_22_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/303569"},{"key":"e_1_2_6_23_2","series-title":"Studies in Mathematics and Its Applications","volume-title":"Numerical Analysis of Variational Inequalities","author":"Glowinski R.","year":"1981"},{"key":"e_1_2_6_24_2","first-page":"125","article-title":"On equilibrium problems","volume":"4","author":"Noor M. A.","year":"2004","journal-title":"Applied Mathematics E-Notes"},{"key":"e_1_2_6_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(93)90058-J"},{"key":"e_1_2_6_26_2","unstructured":"StampacchiaG. Formes bilin\u00e9aires coercitives sur les ensembles convexes 1964 258 4413\u20134416 0166591 ZBL0124.06401."},{"key":"e_1_2_6_27_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/817436"},{"key":"e_1_2_6_28_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/768272"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/437391.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/437391.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/437391","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:39:26Z","timestamp":1718087966000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/437391"}},"subtitle":[],"editor":[{"given":"Rudong","family":"Chen","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/437391"],"URL":"https:\/\/doi.org\/10.1155\/2012\/437391","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2012-03-26","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-03","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-05-30","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"437391"}}