{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T18:29:15Z","timestamp":1676312955258},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2011,2,2]],"date-time":"2011-02-02T00:00:00Z","timestamp":1296604800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2011,12]]},"DOI":"10.1007\/s10898-011-9654-9","type":"journal-article","created":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T04:45:52Z","timestamp":1296535552000},"page":"689-714","source":"Crossref","is-referenced-by-count":8,"title":["Generalized equilibrium problems and fixed point problems for nonexpansive semigroups in Hilbert spaces"],"prefix":"10.1007","volume":"51","author":[{"given":"Uthai","family":"Kamraksa","sequence":"first","affiliation":[]},{"given":"Rabian","family":"Wangkeeree","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,2,2]]},"reference":[{"key":"9654_CR1","first-page":"1511","volume":"280","author":"J.B. Baillon","year":"1975","unstructured":"Baillon J.B.: On theoreme de type ergodique pour les contractions onlineaires dans un espace de Hilbert. C. R. Acad. Sci. Paris 280, 1511\u20131514 (1975)","journal-title":"C. R. Acad. Sci. Paris"},{"key":"9654_CR2","first-page":"123","volume":"63","author":"E. Blum","year":"1994","unstructured":"Blum E., Oettli W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123\u2013145 (1994)","journal-title":"Math. Stud."},{"key":"9654_CR3","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1007\/BF00251595","volume":"24","author":"F.E. Browder","year":"1967","unstructured":"Browder F.E.: Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banch spaces. Arch. Ration. Mech. Anal. 24, 82\u201389 (1967)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"9654_CR4","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0022-247X(67)90085-6","volume":"20","author":"F.E. Browder","year":"1967","unstructured":"Browder F.E., Petryshyn W.V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. Math. Anal. Appl. 20, 197\u2013228 (1967)","journal-title":"J. Math. Anal. Appl."},{"key":"9654_CR5","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1023\/B:JOTA.0000037604.96151.26","volume":"121","author":"O. Chadli","year":"2004","unstructured":"Chadli O., Schaible S., Yao J.C.: Regularized equilibrium problems with an application to noncoercive hemivariational inequalities. J. Optim. Theory Appl. 121, 571\u2013596 (2004)","journal-title":"J. Optim. Theory Appl."},{"key":"9654_CR6","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s10957-009-9628-y","volume":"146","author":"F. Cianciaruso","year":"2010","unstructured":"Cianciaruso F., Marino G., Muglia L.: Iterative methods for equilibrium and fixed point problems for nonexpansive semigroups in Hilbert spaces. J. Optim. Theory Appl. 146, 491\u2013509 (2010)","journal-title":"J. Optim. Theory Appl."},{"key":"9654_CR7","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1080\/01630569808816813","volume":"19","author":"F. Deutsch","year":"1998","unstructured":"Deutsch F., Yamada I.: Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings. Numer. Funct. Anal. Optim. 19, 33\u201356 (1998)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9654_CR8","volume-title":"Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models","author":"F. Giannessi","year":"2001","unstructured":"Giannessi F., Maugeri A., Pardalos P.M.: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Kluwer, Dordrecht (2001)"},{"key":"9654_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jmaa.2000.6733","volume":"246","author":"W. Kaczor","year":"2000","unstructured":"Kaczor W., Kuczumow T., Reich S.: A mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense. J. Math. Anal. Appl. 246, 1\u201327 (2000)","journal-title":"J. Math. Anal. Appl."},{"key":"9654_CR10","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s10957-005-4716-0","volume":"126","author":"I.V. Konnov","year":"2005","unstructured":"Konnov I.V., Schaible S., Yao J.C.: Combined relaxation method for mixed e quilibrium problems. J. Optim. Theory Appl. 126, 309\u2013322 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"9654_CR11","first-page":"37","volume":"9","author":"A. Moudafi","year":"2008","unstructured":"Moudafi A.: Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9, 37\u201343 (2008)","journal-title":"J. Nonlinear Convex Anal."},{"key":"9654_CR12","doi-asserted-by":"crossref","first-page":"3065","DOI":"10.1016\/j.na.2008.04.007","volume":"70","author":"S. Li","year":"2009","unstructured":"Li S., Li L., Su Y.: General iterative methods for a one-parameter nonexpansive semigroup in Hilbert space. J. Nonlinear Anal. 70, 3065\u20133071 (2009)","journal-title":"J. Nonlinear Anal."},{"key":"9654_CR13","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5610(96)00071-8","volume":"78","author":"P.L. Combettes","year":"1997","unstructured":"Combettes P.L., Hirstoaga S.A.: Equilibrium programming using proximal-like algorithms. Math. Program. 78, 29\u201341 (1997)","journal-title":"Math. Program."},{"key":"9654_CR14","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.jmaa.2005.05.028","volume":"318","author":"G. Marino","year":"2006","unstructured":"Marino G., Xu H.K.: A general iterative method for nonexpansive mappings in Hilbert spaces. J. Math. Anal. Appl. 318, 43\u201352 (2006)","journal-title":"J. Math. Anal. Appl."},{"key":"9654_CR15","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1006\/jmaa.1999.6615","volume":"241","author":"A. Moudafi","year":"2000","unstructured":"Moudafi A.: Viscosity approximation methods for fixed-points problems. J. Math. Anal. Appl. 241, 46\u201355 (2000)","journal-title":"J. Math. Anal. Appl."},{"key":"9654_CR16","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1023\/A:1008643727926","volume":"6","author":"F. Liu","year":"1998","unstructured":"Liu F., Nashed M.Z.: Regularization of nonlinear Ill-posed variational inequalities and convergence rates. Set Valued Anal. 6, 313\u2013344 (1998)","journal-title":"Set Valued Anal."},{"key":"9654_CR17","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/j.jmaa.2007.02.044","volume":"336","author":"S. Plubtieng","year":"2007","unstructured":"Plubtieng S., Punpaeng R.: A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces. J. Math. Anal. Appl. 336, 455\u2013469 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"9654_CR18","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/0021-9045(78)90012-6","volume":"24","author":"S. Reich","year":"1978","unstructured":"Reich S.: Almost convergence and nonlinear ergodic theorems. J. Approx. Theory 24, 269\u2013272 (1978)","journal-title":"J. Approx. Theory"},{"key":"9654_CR19","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/0022-247X(83)90168-3","volume":"91","author":"S. Reich","year":"1983","unstructured":"Reich S.: A note on the mean ergodic theorem for nonlinear semigroups. J. Math. Anal. Appl. 91, 547\u2013551 (1983)","journal-title":"J. Math. Anal. Appl."},{"key":"9654_CR20","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1006\/jmaa.1997.5398","volume":"211","author":"T. Shimizu","year":"1997","unstructured":"Shimizu T., Takahashi W.: Strong convergence to common fixed points of families of nonexpansive mappings. J. Math. Anal. Appl. 211, 71\u201383 (1997)","journal-title":"J. Math. Anal. Appl."},{"key":"9654_CR21","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1090\/S0002-9939-06-08435-8","volume":"135","author":"T. Suzuki","year":"2007","unstructured":"Suzuki T.: Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces. Proc. Am. Math. Soc. 135, 99\u2013106 (2007)","journal-title":"Proc. Am. Math. Soc."},{"key":"9654_CR22","doi-asserted-by":"crossref","unstructured":"Wangkeeree, R.: An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings. In: Fixed Point Theory and Applications, Article ID 134148, 17\u00a0pp (2008). doi: 10.1155\/2008\/134148","DOI":"10.1155\/2008\/134148"},{"key":"9654_CR23","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/j.nahs.2009.05.005","volume":"3","author":"R. Wangkeeree","year":"2009","unstructured":"Wangkeeree R., Kamraksa U.: An iterative approximation method for solving a general system of variational inequality problems and mixed equilibrium problems. Nonlinear Anal. Hybrid Syst. 3, 615\u2013630 (2009)","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"9654_CR24","doi-asserted-by":"crossref","unstructured":"Wangkeeree, R., Kamraksa, U.: A general iterative method for solving the variational inequality problem and fixed point Problem of an infinite family of nonexpansive mappings in Hilbert spaces. In: Fixed Point Theory and Applications, vol. 2009, Article ID 369215, 23\u00a0pp. doi: 10.1155\/2009\/369215","DOI":"10.1155\/2009\/369215"},{"key":"9654_CR25","doi-asserted-by":"crossref","unstructured":"Wangkeeree, R., Petrot, N., Wangkeeree, R.: The general iterative methods for nonexpansive mappings in Banach spaces. J. Glob. Optim. doi: 10.1007\/s10898-010-9617-6","DOI":"10.1007\/s10898-010-9617-6"},{"key":"9654_CR26","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1112\/S0024610702003332","volume":"66","author":"H.K. Xu","year":"2002","unstructured":"Xu H.K.: Iterative algorithms for nonlinear operators. J. Lond. Math. Soc. 66, 240\u2013256 (2002)","journal-title":"J. Lond. Math. Soc."},{"key":"9654_CR27","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1023\/A:1023073621589","volume":"116","author":"H.K. Xu","year":"2003","unstructured":"Xu H.K.: An iterative approach to quadratic optimization. J. Optim. Theory Appl. 116, 659\u2013678 (2003)","journal-title":"J. Optim. Theory Appl."},{"key":"9654_CR28","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.jmaa.2004.04.059","volume":"298","author":"H.K. Xu","year":"2004","unstructured":"Xu H.K.: Viscosity approximation methods for nonexpansive mappings. J. Math. Anal. Appl. 298, 279\u2013291 (2004)","journal-title":"J. Math. Anal. Appl."},{"issue":"6","key":"9654_CR29","doi-asserted-by":"crossref","first-page":"1497","DOI":"10.11650\/twjm\/1500404570","volume":"10","author":"L.C. Zeng","year":"2006","unstructured":"Zeng L.C., Wu S.Y., Yao J.C.: Generalized KKM theorem with applications to generalized minimax inequalities and generalized equilibrium problems. Taiwan. J. Math. 10(6), 1497\u20131514 (2006)","journal-title":"Taiwan. J. Math."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-011-9654-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-011-9654-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-011-9654-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T03:48:59Z","timestamp":1559965739000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-011-9654-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,2]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,12]]}},"alternative-id":["9654"],"URL":"https:\/\/doi.org\/10.1007\/s10898-011-9654-9","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,2]]}}}