메뉴 건너뛰기




Volumn 26, Issue 2, 1996, Pages 299-311

Steepest descent approximations for accretive operator equations

Author keywords

Normalized duality map; Quasi accretive operators; Steepest descent approximations

Indexed keywords


EID: 0000892410     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00282-M     Document Type: Article
Times cited : (29)

References (51)
  • 1
    • 84968475614 scopus 로고
    • Nonlinear mappings of nonexpansive and accretive type in Banach spaces
    • BROWDER F. E., Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Am. math. Soc. 73, 875-882 (1967).
    • (1967) Bull. Am. Math. Soc. , vol.73 , pp. 875-882
    • Browder, F.E.1
  • 2
    • 84972539029 scopus 로고
    • Nonlinear semigroups and evolution equations
    • KATO T., Nonlinear semigroups and evolution equations, J. math. Soc. Japan 19, 508-520 (1967).
    • (1967) J. Math. Soc. Japan , vol.19 , pp. 508-520
    • Kato, T.1
  • 3
    • 0042093023 scopus 로고
    • On the derivative of the norm in a Banach space
    • SMUL'YAN V. L., On the derivative of the norm in a Banach space, Dokl. Acad. Nauk. SSSR 27, 255-258 (1940).
    • (1940) Dokl. Acad. Nauk. SSSR , vol.27 , pp. 255-258
    • Smul'yan, V.L.1
  • 4
    • 84968505304 scopus 로고
    • Iterative approximation of fixed points of Lipschitz strictly pseudocontractive mappings
    • CHIDUME C. E., Iterative approximation of fixed points of Lipschitz strictly pseudocontractive mappings, Proc. Am. math. Soc. 99, 283-288 (1987).
    • (1987) Proc. Am. Math. Soc. , vol.99 , pp. 283-288
    • Chidume, C.E.1
  • 5
    • 84972488065 scopus 로고
    • Monotone (nonlinear) operators in Hilbert space
    • MINTY G. J., Monotone (nonlinear) operators in Hilbert space, Duke math. J. 29, 541-546 (1962).
    • (1962) Duke Math. J. , vol.29 , pp. 541-546
    • Minty, G.J.1
  • 6
    • 0002747662 scopus 로고
    • Nonlinear operators and nonlinear equations of evolution in Banach spaces
    • Amer. Math. Soc., Providence RI
    • BROWDER F. E., Nonlinear operators and nonlinear equations of evolution in Banach spaces, in Proc. Symp. Pure Math., Vol. 18, Part 2. Amer. Math. Soc., Providence RI (1976).
    • (1976) Proc. Symp. Pure Math. , vol.18 , Issue.2 PART
    • Browder, F.E.1
  • 7
    • 84968486973 scopus 로고
    • The iterative solution of the equation y ∈ x + Tx for a monotone operator T in Hilbert space
    • BRUCK R. E., The iterative solution of the equation y ∈ x + Tx for a monotone operator T in Hilbert space, Bull. Am. math. Soc. 79, 1258-1261 (1973).
    • (1973) Bull. Am. Math. Soc. , vol.79 , pp. 1258-1261
    • Bruck, R.E.1
  • 9
    • 84968494889 scopus 로고
    • A global existence theorem for autonomous differential equations in Banach spaces
    • MARTIN R. H., A global existence theorem for autonomous differential equations in Banach spaces. Proc. Am. math. Soc. 26, 307-314 (1970).
    • (1970) Proc. Am. Math. Soc. , vol.26 , pp. 307-314
    • Martin, R.H.1
  • 11
    • 0016985417 scopus 로고
    • Monotone operator and the proximal point algorithm
    • ROCKAJELLAR R. T., Monotone operator and the proximal point algorithm, SIAM J. Control. Optim. 14, (5) (1976).
    • (1976) SIAM J. Control. Optim. , vol.14 , Issue.5
    • Rockajellar, R.T.1
  • 13
    • 84971773324 scopus 로고
    • Iterative solution of nonlinear equations of the monotone type in Banach spaces
    • CHIDUME C. E., Iterative solution of nonlinear equations of the monotone type in Banach spaces, Bull. Aust. math. Soc. 42, 21-31 (1990).
    • (1990) Bull. Aust. Math. Soc. , vol.42 , pp. 21-31
    • Chidume, C.E.1
  • 14
    • 84966227927 scopus 로고
    • Approximation of fixed points of strongly pseudo-contractive mappings
    • CHIDUME C. E., Approximation of fixed points of strongly pseudo-contractive mappings, Proc. Am. math. Soc. 120 (2), 545-551 (1994).
    • (1994) Proc. Am. Math. Soc. , vol.120 , Issue.2 , pp. 545-551
    • Chidume, C.E.1
  • 15
    • 51249182697 scopus 로고
    • On the range of accretive operators
    • CRANDALL M. G. & PAZY A., On the range of accretive operators, Israel J. Math. 27, 235-246 (1977).
    • (1977) Israel J. Math. , vol.27 , pp. 235-246
    • Crandall, M.G.1    Pazy, A.2
  • 16
    • 0001399612 scopus 로고
    • Zeros of accretive operators
    • DEIMLING K., Zeros of accretive operators, Manuscripta Math, 13, 365-374 (1974).
    • (1974) Manuscripta Math , vol.13 , pp. 365-374
    • Deimling, K.1
  • 17
    • 0026142372 scopus 로고
    • Iterative approximation of the solution of a locally Lipschitzian equation
    • KANG Zon Bao, Iterative approximation of the solution of a locally Lipschitzian equation, Appl. Math. Mech. (English Ed.) 12 (4), 409-414 (1991); translated from Appl. Math. Mech. 12, (4), 385-389 (1991).
    • (1991) Appl. Math. Mech. (English Ed.) , vol.12 , Issue.4 , pp. 409-414
    • Bao, K.Z.1
  • 18
    • 0026142372 scopus 로고
    • translated
    • KANG Zon Bao, Iterative approximation of the solution of a locally Lipschitzian equation, Appl. Math. Mech. (English Ed.) 12 (4), 409-414 (1991); translated from Appl. Math. Mech. 12, (4), 385-389 (1991).
    • (1991) Appl. Math. Mech. , vol.12 , Issue.4 , pp. 385-389
  • 19
    • 84968510021 scopus 로고
    • Remarks on pseudocontractive mappings
    • KIRK W. A., Remarks on pseudocontractive mappings, Proc. Am. math. Soc. 25, 820-823 (1970).
    • (1970) Proc. Am. Math. Soc. , vol.25 , pp. 820-823
    • Kirk, W.A.1
  • 20
    • 0000593264 scopus 로고
    • Surjectivity theorems for multi-valued mappings of accretive type
    • MORALES C., Surjectivity theorems for multi-valued mappings of accretive type, Commentat. math. Univ. Carol. 26 (2) (1985).
    • (1985) Commentat. Math. Univ. Carol. , vol.26 , Issue.2
    • Morales, C.1
  • 21
    • 0042429722 scopus 로고
    • Global iteration schemes for monotone operators
    • NEVANLINNA O., Global iteration schemes for monotone operators, Nonlinear Analysis 3 (4) (1979).
    • (1979) Nonlinear Analysis , vol.3 , Issue.4
    • Nevanlinna, O.1
  • 22
    • 84971793569 scopus 로고
    • Ishikawa and Mann iteration methods for nonlinear strongly accretive mappings
    • OSILIKE M. O., Ishikawa and Mann iteration methods for nonlinear strongly accretive mappings, Bull Aust. math. Soc. 46, 411-422 (1992).
    • (1992) Bull Aust. Math. Soc. , vol.46 , pp. 411-422
    • Osilike, M.O.1
  • 24
    • 0041868512 scopus 로고
    • An iterative procedure for constructing zeros of accretive sets in Banach space
    • REICH S., An iterative procedure for constructing zeros of accretive sets in Banach space, Nonlinear Analysis 2, 85-92 (1978).
    • (1978) Nonlinear Analysis , vol.2 , pp. 85-92
    • Reich, S.1
  • 25
    • 0000137205 scopus 로고
    • Constructive techniques for accretive and monotone operators
    • Academic Press, New York
    • REICH S., Constructive techniques for accretive and monotone operators, in Applied Nonlinear Analisis, pp. 335-345. Academic Press, New York (1979).
    • (1979) Applied Nonlinear Analisis , pp. 335-345
    • Reich, S.1
  • 26
    • 0000040468 scopus 로고
    • Constructing zeros of accretive operators, I, II
    • REICH S., Constructing zeros of accretive operators, I, II, Applic. Analysis 8, 349-352 (1979); Applic. Analysis 9, 159-163 (1979).
    • (1979) Applic. Analysis , vol.8 , pp. 349-352
    • Reich, S.1
  • 27
    • 84950221852 scopus 로고
    • REICH S., Constructing zeros of accretive operators, I, II, Applic. Analysis 8, 349-352 (1979); Applic. Analysis 9, 159-163 (1979).
    • (1979) Applic. Analysis , vol.9 , pp. 159-163
  • 28
    • 84985311471 scopus 로고
    • On a theorem of C. E. Chidume concerning the iterative approximation of fixed points
    • SCHU J., On a theorem of C. E. Chidume concerning the iterative approximation of fixed points, Math. Nachr. 153, 313-319 (1991).
    • (1991) Math. Nachr. , vol.153 , pp. 313-319
    • Schu, J.1
  • 29
    • 0001944173 scopus 로고
    • Iterative construction of fixed points of strictly pseudocontractive mappings
    • SCHU J., Iterative construction of fixed points of strictly pseudocontractive mappings, Applic. Analysis 40, 67-72 (1991).
    • (1991) Applic. Analysis , vol.40 , pp. 67-72
    • Schu, J.1
  • 30
    • 0039269495 scopus 로고
    • On the convergence of the method of steepest descent for nonlinear equations
    • VAINBERG M. M., On the convergence of the method of steepest descent for nonlinear equations, Sibirsk. Math. Z. 2, 201-220 (1961).
    • (1961) Sibirsk. Math. Z. , vol.2 , pp. 201-220
    • Vainberg, M.M.1
  • 32
    • 50749132985 scopus 로고
    • Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
    • XU ZONGBEN, & ROACH G. F., Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces, J. math. Analysis Applic. 157, 189-210 (1991).
    • (1991) J. Math. Analysis Applic. , vol.157 , pp. 189-210
    • Xu, Z.1    Roach, G.F.2
  • 33
    • 0042593883 scopus 로고
    • On the steepest descent approximation to solutions of nonlinear strongly accretive operator equations
    • XU ZONGBEN, ZHANG BO & ROACH G. F., On the steepest descent approximation to solutions of nonlinear strongly accretive operator equations, J. Comput. Math. 1, (2) (1992).
    • (1992) J. Comput. Math. , vol.1 , Issue.2
    • Xu, Z.1    Zhang, B.2    Roach, G.F.3
  • 34
    • 0001285910 scopus 로고
    • A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations
    • XU ZONGBEN & ROACH G. F., A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations, J. math. Analysis Applic. 167, 340-354 (1992).
    • (1992) J. Math. Analysis Applic. , vol.167 , pp. 340-354
    • Xu, Z.1    Roach, G.F.2
  • 36
    • 0041591960 scopus 로고
    • A class of iteration methods for a strongly monotone operator equation and application to finite element approximate solution of nonlinear elliptic boundary value problem
    • YOU ZHAO & XU ZONGBEN, A class of iteration methods for a strongly monotone operator equation and application to finite element approximate solution of nonlinear elliptic boundary value problem. J Comput. Math. 2, 112-121 (1984).
    • (1984) J Comput. Math. , vol.2 , pp. 112-121
    • You, Z.1    Xu, Z.2
  • 37
    • 0041591963 scopus 로고
    • The region contraction algorithm for constructing zeros of a quasi-strongly monotone operator
    • YOU ZHAOYONG, XU ZONGBEN & LIU KUNKUN, The region contraction algorithm for constructing zeros of a quasi-strongly monotone operator, J. Engr. Math. 1, 11-28 (1984).
    • (1984) J. Engr. Math. , vol.1 , pp. 11-28
    • You, Z.1    Xu, Z.2    Liu, K.3
  • 38
    • 84966213287 scopus 로고
    • The closure of the numerical range contains the spectrum
    • ZARANTONELLO E. H., The closure of the numerical range contains the spectrum, Bull. Am. math. Soc. 70, 781-783 (1964).
    • (1964) Bull. Am. Math. Soc. , vol.70 , pp. 781-783
    • Zarantonello, E.H.1
  • 39
    • 0042593885 scopus 로고
    • The solution of nonlinear equations with monotone transformations
    • FONAREV A. A., The solution of nonlinear equations with monotone transformations (Russian), Diff. Urav. 14, (A) (1978).
    • (1978) Diff. Urav. , vol.14 , Issue.A
    • Fonarev, A.A.1
  • 41
    • 0002828027 scopus 로고
    • Hanner inequality and convergence of iteration procedures
    • Izvestiya
    • TRUVNIKOV Yu. V., Hanner inequality and convergence of iteration procedures, Soviet Math. (Izvestiya) 31,(7) 74-83 (1987).
    • (1987) Soviet Math. , vol.31 , Issue.7 , pp. 74-83
    • Truvnikov, Yu.V.1
  • 42
    • 0000243812 scopus 로고
    • Approximation von Fixpunkten streng pseudokontraktiver operatoren
    • BETHKE M., Approximation von Fixpunkten streng pseudokontraktiver operatoren (Approximation of fixed points of strongly pseudocontractive operators), Math. Naturwiss. Fak. 27 (2), 263-270 (1989).
    • (1989) Math. Naturwiss. Fak. , vol.27 , Issue.2 , pp. 263-270
    • Bethke, M.1
  • 43
    • 0003317987 scopus 로고
    • Geometry of Banach spaces-selected topics
    • Springer, New York
    • DIESTEL J., Geometry of Banach spaces-selected topics, in Lecture Notes in Mathematics, Vol. 485. Springer, New York (1975).
    • (1975) Lecture Notes in Mathematics , vol.485
    • Diestel, J.1
  • 46
    • 51249185817 scopus 로고
    • Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces
    • NEVANLINNA O. & REICH S., Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel J. Math. 32, 44-58 (1979).
    • (1979) Israel J. Math. , vol.32 , pp. 44-58
    • Nevanlinna, O.1    Reich, S.2
  • 47
    • 0001011342 scopus 로고
    • Nonlinear monotone and accretive operators in Banach spaces
    • BROWDER F. E., Nonlinear monotone and accretive operators in Banach spaces, Proc. natn. Acad. Sci. U.S-A. 61, 388-393 (1968).
    • (1968) Proc. Natn. Acad. Sci. U.S-A. , vol.61 , pp. 388-393
    • Browder, F.E.1
  • 48
    • 0000827660 scopus 로고
    • Construction of fixed points of nonlinear mappings in Hubert space
    • BROWDER F. E. & PETRYSHYN W. V., Construction of fixed points of nonlinear mappings in Hubert space, J. math. Analysis Applic. 20, 197-228 (1967).
    • (1967) J. Math. Analysis Applic. , vol.20 , pp. 197-228
    • Browder, F.E.1    Petryshyn, W.V.2
  • 49
    • 0002364055 scopus 로고
    • On the Mann iteration process
    • DOTSON W. G., On the Mann iteration process. Trans Am. math. Soc. 149, 65-73 (1970).
    • (1970) Trans Am. Math. Soc. , vol.149 , pp. 65-73
    • Dotson, W.G.1
  • 50
    • 84968499765 scopus 로고
    • Fixed points and interation of a nonexpansive mapping on a Banach space
    • ISHIKAWA S., Fixed points and interation of a nonexpansive mapping on a Banach space, Proc. Am. math. Soc. 59, 65-71 (1976).
    • (1976) Proc. Am. Math. Soc. , vol.59 , pp. 65-71
    • Ishikawa, S.1
  • 51
    • 84968519140 scopus 로고
    • Approximating fixed points of nonexpansive mappings
    • SENTER H. F. & DOTSON W. G., Approximating fixed points of nonexpansive mappings, Proc. Am. math. Soc. 44, 375-380 (1974).
    • (1974) Proc. Am. Math. Soc. , vol.44 , pp. 375-380
    • Senter, H.F.1    Dotson, W.G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.