메뉴 건너뛰기




Volumn 15, Issue 3, 2007, Pages 297-306

A convex-analytical approach to extension results for n-cyclically monotone operators

Author keywords

Convex analysis; Cyclic monotonicity; Debrunner Flor extension; Fenchel Rockafellar duality; Fitzpatrick functions; Monotone operator

Indexed keywords


EID: 34547565727     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11228-006-0029-1     Document Type: Article
Times cited : (9)

References (27)
  • 2
    • 34250724621 scopus 로고    scopus 로고
    • Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings
    • Bauschke, H.H.: Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings. Proc. Amer. Math. Soc. 135, 135-139 (2007)
    • (2007) Proc. Amer. Math. Soc. , vol.135 , pp. 135-139
    • Bauschke, H.H.1
  • 3
    • 49449086907 scopus 로고    scopus 로고
    • Fitzpatrick functions and continuous linear monotone operators
    • to appear
    • Bauschke, H.H., Borwein, J.M., Wang, X.: Fitzpatrick functions and continuous linear monotone operators. SIAM J. Optim. (to appear)
    • SIAM J. Optim.
    • Bauschke, H.H.1    Borwein, J.M.2    Wang, X.3
  • 4
    • 34547606127 scopus 로고    scopus 로고
    • Fitzpatrick functions: Inequalities, examples and remarks on a problem by S. Fitzpatrick
    • Bauschke, H.H., McLaren, D.A., Sendov, H.S.: Fitzpatrick functions: inequalities, examples and remarks on a problem by S. Fitzpatrick. J. Convex Anal. (in press)
    • J. Convex Anal. (In Press)
    • Bauschke, H.H.1    McLaren, D.A.2    Sendov, H.S.3
  • 8
    • 33846488416 scopus 로고    scopus 로고
    • On the Fitzpatrick family associated to some subdifferentials
    • Burachik, R.S., Fitzpatrick, S.: On the Fitzpatrick family associated to some subdifferentials. J. Nonlinear Convex Anal. 6, 165-171 (2005)
    • (2005) J. Nonlinear Convex Anal. , vol.6 , pp. 165-171
    • Burachik, R.S.1    Fitzpatrick, S.2
  • 9
    • 0036034569 scopus 로고    scopus 로고
    • Maximal monotone operators, convex functions and a special family of enlargements
    • Burachik, R.S., Svaiter, B.F.: Maximal monotone operators, convex functions and a special family of enlargements. Set-Valued Anal. 10, 297-316 (2002)
    • (2002) Set-Valued Anal. , vol.10 , pp. 297-316
    • Burachik, R.S.1    Svaiter, B.F.2
  • 10
    • 0042745499 scopus 로고    scopus 로고
    • Maximal monotonicity, conjugation and the duality product
    • Burachik, R.S., Svaiter, B.F.: Maximal monotonicity, conjugation and the duality product. Proc. Amer. Math. Soc. 131, 2379-2383 (2003)
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 2379-2383
    • Burachik, R.S.1    Svaiter, B.F.2
  • 11
    • 0010757594 scopus 로고
    • Ein Erweiterungssatz für monotone Mengen
    • Debrunner, H., Flor, P.: Ein Erweiterungssatz für monotone Mengen. Arch. Math. 15, 445-447 (1964)
    • (1964) Arch. Math. , vol.15 , pp. 445-447
    • Debrunner, H.1    Flor, P.2
  • 12
    • 0038231522 scopus 로고
    • Representing monotone operators by convex functions
    • Workshop/Miniconference on Functional Analysis and Optimization (Canberra 1988) Australian National University, Canberra, Australia
    • Fitzpatrick, S.: Representing monotone operators by convex functions. In: Workshop/Miniconference on Functional Analysis and Optimization (Canberra 1988). In: Proceedings of the Centre for Mathematical Analysis, vol. 20, pp. 59-65. Australian National University, Canberra, Australia (1988)
    • (1988) Proceedings of the Centre for Mathematical Analysis , vol.20 , pp. 59-65
    • Fitzpatrick, S.1
  • 15
    • 18744404859 scopus 로고    scopus 로고
    • Monotone operators representable by l.s.c. convex functions
    • Martínez-Legaz, J.-E., Svaiter, B.F.: Monotone operators representable by l.s.c. convex functions. Set.-Valued Anal. 13, 21-46 (2005)
    • (2005) Set-Valued Anal. , vol.13 , pp. 21-46
    • Martínez-Legaz, J.-E.1    Svaiter, B.F.2
  • 16
  • 17
    • 84972488065 scopus 로고
    • Monotone (nonlinear) operators in Hilbert space
    • Minty, G.J.: Monotone (nonlinear) operators in Hilbert space. Duke Math. J. 29, 341-346 (1962)
    • (1962) Duke Math. J. , vol.29 , pp. 341-346
    • Minty, G.J.1
  • 18
    • 4243129234 scopus 로고    scopus 로고
    • The relevance of convex analysis for the study of monotonicity
    • Penot, J.P.: The relevance of convex analysis for the study of monotonicity. Nonlinear Anal. 58, 855-871 (2004)
    • (2004) Nonlinear Anal. , vol.58 , pp. 855-871
    • Penot, J.P.1
  • 19
    • 24944580357 scopus 로고    scopus 로고
    • Fenchel duality, Fitzpatrick functions and the Kirszbraun-Valentine extension theorem
    • Reich, S., Simons, S.: Fenchel duality, Fitzpatrick functions and the Kirszbraun-Valentine extension theorem. Proc. Amer. Math. Soc. 133, 2657-2660 (2005)
    • (2005) Proc. Amer. Math. Soc. , vol.133 , pp. 2657-2660
    • Reich, S.1    Simons, S.2
  • 20
    • 0004267646 scopus 로고
    • Princeton University Press Princeton, NJ
    • Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, NJ (1970)
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 23
    • 5644292074 scopus 로고    scopus 로고
    • A new proof for Rockafellar's characterization of maximal monotone operators
    • Simons, S., Zǎlinescu, C.: A new proof for Rockafellar's characterization of maximal monotone operators. Proc. Amer. Math. Soc. 132, 2969-2972 (2004)
    • (2004) Proc. Amer. Math. Soc. , vol.132 , pp. 2969-2972
    • Simons, S.1    Zǎlinescu, C.2
  • 24
    • 33745936299 scopus 로고    scopus 로고
    • Fenchel duality, Fitzpatrick functions and maximal monotonicity
    • Simons, S., Zǎlinescu, C.: Fenchel duality, Fitzpatrick functions and maximal monotonicity. J. Nonlinear Convex Anal. 6, 1-22 (2005)
    • (2005) J. Nonlinear Convex Anal. , vol.6 , pp. 1-22
    • Simons, S.1    Zǎlinescu, C.2
  • 26
    • 34547611509 scopus 로고    scopus 로고
    • A maximality theorem for the sum of maximal monotone operators in non-reflexive Banach spaces
    • Voisei, M.D.: A maximality theorem for the sum of maximal monotone operators in non-reflexive Banach spaces. Math. Sci. Res. J. 10, 36-41 (2006)
    • (2006) Math. Sci. Res. J. , vol.10 , pp. 36-41
    • Voisei, M.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.