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Volumn 141, Issue 1, 2009, Pages 75-91

Hybrid steepest descent methods for zeros of nonlinear operators with applications to variational inequalities

Author keywords

Hybrid steepest descent method; Uniformly smooth Banach spaces; Variational inequalities; strongly accretive mappings

Indexed keywords

BANACH SPACES; MAPPING; MATHEMATICAL OPERATORS; STEEPEST DESCENT METHOD; VARIATIONAL TECHNIQUES;

EID: 62949086133     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-008-9501-4     Document Type: Article
Times cited : (11)

References (20)
  • 1
    • 0003117605 scopus 로고
    • Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces
    • K.K. Tan H.K. Xu 1993 Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces J. Math. Anal. Appl. 178 9 21
    • (1993) J. Math. Anal. Appl. , vol.178 , pp. 9-21
    • Tan, K.K.1    Xu, H.K.2
  • 2
    • 0031128528 scopus 로고    scopus 로고
    • Error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth Banach spaces
    • L.C. Zeng 1997 Error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth Banach spaces J. Math. Anal. Appl. 209 67 80
    • (1997) J. Math. Anal. Appl. , vol.209 , pp. 67-80
    • Zeng, L.C.1
  • 3
    • 0032014653 scopus 로고    scopus 로고
    • Iterative approximation of solutions to nonlinear equations of strongly accretive operators in Banach spaces
    • L.C. Zeng 1998 Iterative approximation of solutions to nonlinear equations of strongly accretive operators in Banach spaces Nonlinear Anal. 31 589 598
    • (1998) Nonlinear Anal. , vol.31 , pp. 589-598
    • Zeng, L.C.1
  • 4
    • 0041868512 scopus 로고
    • An iterative procedure for constructing zeros of accretive sets in Banach spaces
    • S. Reich 1978 An iterative procedure for constructing zeros of accretive sets in Banach spaces Nonlinear Anal. 2 85 92
    • (1978) Nonlinear Anal. , vol.2 , pp. 85-92
    • Reich, S.1
  • 5
    • 0000137205 scopus 로고
    • Constructive techniques for accretive and monotone operators
    • Academic Press San Diego
    • Reich, S.: Constructive techniques for accretive and monotone operators. In: Applied Nonlinear Analysis, pp. 335-345. Academic Press, San Diego (1979)
    • (1979) Applied Nonlinear Analysis , pp. 335-345
    • Reich, S.1
  • 6
    • 0001285910 scopus 로고
    • A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations
    • Z.B. Xu G.F. Roach 1992 A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations J. Math. Anal. Appl. 167 340 354
    • (1992) J. Math. Anal. Appl. , vol.167 , pp. 340-354
    • Xu, Z.B.1    Roach, G.F.2
  • 7
    • 22844453989 scopus 로고    scopus 로고
    • Convergence of the steepest descent method for accretive operators
    • C.H. Morales C.E. Chidume 1999 Convergence of the steepest descent method for accretive operators Proc. Am. Math. Soc. 127 3677 3683
    • (1999) Proc. Am. Math. Soc. , vol.127 , pp. 3677-3683
    • Morales, C.H.1    Chidume, C.E.2
  • 8
    • 0031999680 scopus 로고    scopus 로고
    • Minimizing certain convex functions over the intersection of the fixed-point sets of nonexpansive mappings
    • F. Deutsch I. Yamada 1998 Minimizing certain convex functions over the intersection of the fixed-point sets of nonexpansive mappings Numer. Funct. Anal. Optim. 19 33 56
    • (1998) Numer. Funct. Anal. Optim. , vol.19 , pp. 33-56
    • Deutsch, F.1    Yamada, I.2
  • 9
    • 0344512422 scopus 로고    scopus 로고
    • Convergence of hybrid steepest-descent methods for variational inequalities
    • H.K. Xu T.H. Kim 2003 Convergence of hybrid steepest-descent methods for variational inequalities J. Optim. Theory Appl. 119 185 201
    • (2003) J. Optim. Theory Appl. , vol.119 , pp. 185-201
    • Xu, H.K.1    Kim, T.H.2
  • 10
    • 77956693893 scopus 로고    scopus 로고
    • The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed-point sets of nonexpansive mappings
    • North-Holland Amsterdam
    • Yamada, I.: The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed-point sets of nonexpansive mappings. In: Butnariu, D., Censor, Y., Reich, S. (eds.) Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, pp. 473-504. North-Holland, Amsterdam (2001)
    • (2001) Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications , pp. 473-504
    • Yamada, I.1    Butnariu, D.2    Censor, Y.3    Reich, S.4
  • 11
    • 0042745484 scopus 로고    scopus 로고
    • Approximation methods for nonlinear operator equations
    • C.E. Chidume H. Zegeye 2003 Approximation methods for nonlinear operator equations Proc. Am. Math. Soc. 131 2467 2478
    • (2003) Proc. Am. Math. Soc. , vol.131 , pp. 2467-2478
    • Chidume, C.E.1    Zegeye, H.2
  • 14
    • 0000743842 scopus 로고
    • Variational inequalities and the pricing of American options
    • P. Jaillet D. Lamberton B. Lapeyre 1990 Variational inequalities and the pricing of American options Acta Appl. Math. 21 263 289
    • (1990) Acta Appl. Math. , vol.21 , pp. 263-289
    • Jaillet, P.1    Lamberton, D.2    Lapeyre, B.3
  • 16
    • 0001021845 scopus 로고
    • Variational inequalities with generalized monotone operators
    • J.C. Yao 1994 Variational inequalities with generalized monotone operators Math. Oper. Res. 49 691 705
    • (1994) Math. Oper. Res. , vol.49 , pp. 691-705
    • Yao, J.C.1
  • 19
    • 33847646305 scopus 로고    scopus 로고
    • Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities
    • L.C. Zeng N.C. Wong J.C. Yao 2006 Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities J. Optim. Theory Appl. 132 51 69
    • (2006) J. Optim. Theory Appl. , vol.132 , pp. 51-69
    • Zeng, L.C.1    Wong, N.C.2    Yao, J.C.3
  • 20
    • 29144447891 scopus 로고    scopus 로고
    • Convergence of hybrid steepest-descent methods for generalized variational inequalities
    • L.C. Zeng N.C. Wong J.C. Yao 2006 Convergence of hybrid steepest-descent methods for generalized variational inequalities Acta Math. Sin. Engl. Ser. 22 1 12
    • (2006) Acta Math. Sin. Engl. Ser. , vol.22 , pp. 1-12
    • Zeng, L.C.1    Wong, N.C.2    Yao, J.C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.