{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:23:19Z","timestamp":1773231799430,"version":"3.50.1"},"publisher-location":"New York, NY","reference-count":29,"publisher":"Springer New York","isbn-type":[{"value":"9781441995681","type":"print"},{"value":"9781441995698","type":"electronic"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-1-4419-9569-8_15","type":"book-chapter","created":{"date-parts":[[2011,5,26]],"date-time":"2011-05-26T19:17:16Z","timestamp":1306437436000},"page":"301-316","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":57,"title":["Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces"],"prefix":"10.1007","author":[{"given":"Simeon","family":"Reich","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shoham","family":"Sabach","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,5,9]]},"reference":[{"key":"15_CR1_15","first-page":"15","volume-title":"Theory and Applications of Nonlinear Operators of Accretive and Monotone Type","author":"YI Alber","year":"1996","unstructured":"Alber, Y.I.: Metric and generalized projection operators in Banach spaces: properties and applications. In: A.G. Kartsatos (ed.) Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, pp. 15\u201350. Marcel Dekker, New York (1996)"},{"key":"15_CR2_15","first-page":"27","volume":"4","author":"HH Bauschke","year":"1997","unstructured":"Bauschke, H.H., Borwein, J.M.: Legendre functions and the method of random Bregman projections. J. Convex Anal. 4, 27\u201367 (1997)","journal-title":"J. Convex Anal."},{"key":"15_CR3_15","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1142\/S0219199701000524","volume":"3","author":"HH Bauschke","year":"2001","unstructured":"Bauschke, H.H., Borwein, J.M., Combettes, P.L.: Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces. Comm. Contemp. Math. 3, 615\u2013647 (2001)","journal-title":"Comm. Contemp. Math."},{"key":"15_CR4_15","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1137\/S0363012902407120","volume":"42","author":"HH Bauschke","year":"2003","unstructured":"Bauschke, H.H., Borwein, J.M., Combettes, P.L.: Bregman monotone optimization algorithms. SIAM J. Control Optim. 42, 596\u2013636 (2003)","journal-title":"SIAM J. Control Optim."},{"key":"15_CR5_15","doi-asserted-by":"publisher","first-page":"3757","DOI":"10.1090\/S0002-9939-03-07050-3","volume":"131","author":"HH Bauschke","year":"2003","unstructured":"Bauschke, H.H., Combettes, P.L.: Construction of best Bregman approximations in reflexive Banach spaces. Proc. Amer. Math. Soc. 131, 3757\u20133766 (2003)","journal-title":"Proc. Amer. Math. Soc."},{"key":"15_CR6_15","unstructured":"Bauschke, H.H., Wang, X., Yao, L.: General resolvents for monotone operators: characterization and extension. Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Medical Physics Publishing, Madison, WI, USA, 57\u201374 (2010)"},{"key":"15_CR7_15","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems","author":"JF Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New\u00a0York (2000)"},{"key":"15_CR8_15","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/0041-5553(67)90040-7","volume":"7","author":"LM Bregman","year":"1967","unstructured":"Bregman, L.M.: The relaxation method of finding a common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. and Math. Phys. 7, 200\u2013217 (1967)","journal-title":"USSR Comput. Math. and Math. Phys."},{"key":"15_CR9_15","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1007\/BF00251595","volume":"24","author":"FE Browder","year":"1967","unstructured":"Browder, F.E.: Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces. Arch. Rational. Mech. Anal. 24, 82\u201390 (1967)","journal-title":"Arch. Rational. Mech. Anal."},{"key":"15_CR10_15","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2140\/pjm.1973.47.341","volume":"47","author":"RE Bruck","year":"1973","unstructured":"Bruck, R.E.: Nonexpansive projections on subsets of Banach spaces. Pacific J. Math. 47, 341\u2013355 (1973)","journal-title":"Pacific J. Math."},{"key":"15_CR11_15","first-page":"459","volume":"3","author":"RE Bruck","year":"1977","unstructured":"Bruck, R.E., Reich, S.: Nonexpansive projections and resolvents of accretive operators in Banach spaces. Houston J. Math. 3, 459\u2013470 (1977)","journal-title":"Houston J. Math."},{"key":"15_CR12_15","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-4066-9","volume-title":"Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization","author":"D Butnariu","year":"2000","unstructured":"Butnariu, D., Iusem, A.N.: Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization. Kluwer Academic Publishers, Dordrecht (2000)"},{"key":"15_CR13_15","doi-asserted-by":"crossref","unstructured":"Butnariu, D., Resmerita, E.: Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces. Abstr. Appl. Anal. 2006, 1\u201339, Art. ID 84919 (2006)","DOI":"10.1155\/AAA\/2006\/84919"},{"key":"15_CR14_15","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1023\/A:1008654413997","volume":"8","author":"D Butnariu","year":"1997","unstructured":"Butnariu, D., Censor, Y., Reich, S.: Iterative averaging of entropic projections for solving stochastic convex feasibility problems. Comput. Optim. Appl. 8, 21\u201339 (1997)","journal-title":"Comput. Optim. Appl."},{"key":"15_CR15_15","first-page":"319","volume":"7","author":"D Butnariu","year":"2000","unstructured":"Butnariu, D., Iusem, A.N., Resmerita, E.: Total convexity for powers of the norm in uniformly convex Banach spaces. J. Convex Anal. 7, 319\u2013334 (2000)","journal-title":"J. Convex Anal."},{"key":"15_CR16_15","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/BF00934676","volume":"34","author":"Y Censor","year":"1981","unstructured":"Censor, Y., Lent, A.: An iterative row-action method for interval convex programmings. J.\u00a0Optim. Theory Appl. 34, 321\u2013353 (1981)","journal-title":"J. Optim. Theory Appl."},{"key":"15_CR17_15","volume-title":"Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings","author":"K Goebel","year":"1984","unstructured":"Goebel, K., Reich, S.: Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. Marcel Dekker, New York (1984)"},{"key":"15_CR18_15","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1090\/S0002-9904-1967-11864-0","volume":"73","author":"B Halpern","year":"1967","unstructured":"Halpern, B.: Fixed points of nonexpanding maps. Bull. Amer. Math. Soc. 73, 957\u2013961 (1967)","journal-title":"Bull. Amer. Math. Soc."},{"key":"15_CR19_15","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1155\/S1085337504309036","volume":"3","author":"F Kohsaka","year":"2004","unstructured":"Kohsaka, F., Takahashi, W.: Strong convergence of an iterative sequence for maximal monotone operators in a Banach space. Abstr. Appl. Anal. 3, 239\u2013249 (2004)","journal-title":"Abstr. Appl. Anal."},{"key":"15_CR20_15","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1137\/070688717","volume":"19","author":"F Kohsaka","year":"2008","unstructured":"Kohsaka, F., Takahashi, W.: Existence and approximation of fixed points of firmly nonexpansive-type mappings in Banach spaces. SIAM J. Control Optim. 19, 824\u2013835 (2008)","journal-title":"SIAM J. Control Optim."},{"key":"15_CR21_15","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1007\/s00013-008-2545-8","volume":"21","author":"F. Kohsaka","year":"2008","unstructured":"Kohsaka, F., Takahashi, W.: Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces. Arch. Math. (Basel) 21, 166\u2013177 (2008)","journal-title":"Arch. Math. (Basel)"},{"key":"15_CR22_15","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1215\/S0012-7094-62-02933-2","volume":"29","author":"GJ Minty","year":"1962","unstructured":"Minty, G.J.: Monotone (nonlinear) operators in Hilbert space. Duke Math. J. 29, 341\u2013346 (1962)","journal-title":"Duke Math. J."},{"key":"15_CR23_15","doi-asserted-by":"crossref","first-page":"273","DOI":"10.24033\/bsmf.1625","volume":"93","author":"JJ Moreau","year":"1965","unstructured":"Moreau, J.J.: Proximit\u00e9 et dualit\u00e9 dans un espace hilbertien. Bull. Soc. Math. France 93, 273\u2013299 (1965)","journal-title":"Bull. Soc. Math. France"},{"key":"15_CR24_15","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/0022-247X(79)90024-6","volume":"67","author":"S Reich","year":"1979","unstructured":"Reich, S.: Weak convergence theorems for nonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 67, 274\u2013276 (1979)","journal-title":"J. Math. Anal. Appl."},{"key":"15_CR25_15","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0022-247X(80)90323-6","volume":"75","author":"S Reich","year":"1980","unstructured":"Reich, S.: Strong convergence theorems for resolvents of accretive operators in Banach spaces. J. Math. Anal. Appl. 75, 287\u2013292 (1980)","journal-title":"J. Math. Anal. Appl."},{"key":"15_CR26_15","first-page":"313","volume-title":"Theory and Applications of Nonlinear Operators of Accretive and Monotone Type","author":"S Reich","year":"1996","unstructured":"Reich, S.: A weak convergence theorem for the alternating method with Bregman distances. In: A.G. Kartsatos (ed.) Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, pp. 313\u2013318. Marcel Dekker, New York (1996)"},{"key":"15_CR27_15","first-page":"471","volume":"10","author":"S Reich","year":"2009","unstructured":"Reich, S., Sabach, S.: A strong convergence theorem for a proximal-type algorithm in reflexive Banach spaces. J. Nonlinear Convex Anal. 10, 471\u2013485 (2009)","journal-title":"J. Nonlinear Convex Anal."},{"key":"15_CR28_15","first-page":"1","volume":"11","author":"E Resmerita","year":"2004","unstructured":"Resmerita, E.: On total convexity, Bregman projections and stability in Banach spaces. J.\u00a0Convex Anal. 11, 1\u201316 (2004)","journal-title":"Bregman projections and stability in Banach spaces. J. Convex Anal."},{"key":"15_CR29_15","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1090\/S0002-9947-1966-0192318-X","volume":"123","author":"RT Rockafellar","year":"1966","unstructured":"Rockafellar, R.T.: Level sets and continuity of conjugate convex functions. Trans. Amer. Math. Soc 123, 46\u201363 (1966)","journal-title":"Trans. Amer. Math. Soc"}],"container-title":["Springer Optimization and Its Applications","Fixed-Point Algorithms for Inverse Problems in Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4419-9569-8_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T23:23:50Z","timestamp":1674861830000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-1-4419-9569-8_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9781441995681","9781441995698"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-1-4419-9569-8_15","relation":{},"ISSN":["1931-6828"],"issn-type":[{"value":"1931-6828","type":"print"}],"subject":[],"published":{"date-parts":[[2011]]},"assertion":[{"value":"9 May 2011","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}