메뉴 건너뛰기




Volumn 27, Issue 3, 2009, Pages 319-330

On the local convergence of a two-step steffensen-type method for solving generalized equations

Author keywords

Aubin continuity; Banach space; Divided difference; Generalized equation; H lder continuity; Radius of convergence; Setvalued map; Steffensen's method

Indexed keywords


EID: 70949084393     PISSN: 07160917     EISSN: 07176279     Source Type: Journal    
DOI: 10.4067/S0716-09172008000300007     Document Type: Article
Times cited : (3)

References (22)
  • 1
    • 17944380525 scopus 로고    scopus 로고
    • Convergence and numerical analysis of a family of two- step Steffensen's methods
    • S. Amat, S. Busquier, Convergence and numerical analysis of a family of two- step Steffensen's methods, Comput. and Math. with Appl., 49, pp. 13-22, (2005).
    • (2005) Comput. and Math. with Appl. , vol.49 , pp. 13-22
    • Amat, S.1    Busquier, S.2
  • 2
    • 17944382757 scopus 로고    scopus 로고
    • A new convergence theorem for Steffensen's method on Banach spaces and applications
    • I. K. Argyros, A new convergence theorem for Steffensen's method on Banach spaces and applications, Southwest J. of Pure and Appl. Math., 01, pp. 23-29, (1997).
    • (1997) Southwest J. of Pure and Appl. Math. , vol.1 , pp. 23-29
    • Argyros, I.K.1
  • 3
    • 35348959329 scopus 로고    scopus 로고
    • On the solution of generalized equations using m (m ≥ 2) Fréchet differential operators
    • I. K. Argyros, On the solution of generalized equations using m (m ≥ 2) Fréchet differential operators, Comm. Appl. Nonlinear Anal., 09, pp. 85-89, (2002).
    • (2002) Comm. Appl. Nonlinear Anal. , vol.9 , pp. 85-89
    • Argyros, I.K.1
  • 4
    • 10144254426 scopus 로고    scopus 로고
    • A unifying local-semilocal convergence analysis and applications for Newton-like methods
    • I. K. Argyros, A unifying local-semilocal convergence analysis and applications for Newton-like methods, J. Math. Anal. Appl., 298, pp. 374-397, (2004).
    • (2004) J. Math. Anal. Appl. , vol.298 , pp. 374-397
    • Argyros, I.K.1
  • 5
    • 43149101104 scopus 로고    scopus 로고
    • On the approximation of strongly regular solutions for generalized equations
    • I. K. Argyros, On the approximation of strongly regular solutions for generalized equations, Comm. Appl. Nonlinear Anal., 12, pp. 97-107, (2005).
    • (2005) Comm. Appl. Nonlinear Anal. , vol.12 , pp. 97-107
    • Argyros, I.K.1
  • 6
    • 84967638928 scopus 로고    scopus 로고
    • Approximate solution of operator equations with applications
    • New Jersey, U. S. A
    • I. K. Argyros, Approximate solution of operator equations with applications, World Scientific Publ. Comp., New Jersey, U. S. A., (2005).
    • (2005) World Scientific Publ. Comp.
    • Argyros, I.K.1
  • 7
    • 39449116406 scopus 로고    scopus 로고
    • An improved convergence analysis of a superquadratic method for solving generalized equations
    • I. K. Argyros, An improved convergence analysis of a superquadratic method for solving generalized equations, Rev. Colombiana Math., 40, pp. 65-73, (2006).
    • (2006) Rev. Colombiana Math. , vol.40 , pp. 65-73
    • Argyros, I.K.1
  • 9
    • 0000410841 scopus 로고
    • An inverse function theorem for set-valued maps
    • A. L. Dontchev, W. W. Hager, An inverse function theorem for set-valued maps, Proc. Amer. Math. Soc., 121, pp. 481-489, (1994).
    • (1994) Proc. Amer. Math. Soc. , vol.121 , pp. 481-489
    • Dontchev, A.L.1    Hager, W.W.2
  • 10
    • 33646540696 scopus 로고    scopus 로고
    • Stability of a cubically convergent method for generalized equations
    • M. H. Geoffroy, S. Hilout, A. Piétrus, Stability of a cubically convergent method for generalized equations, Set-Valued Anal., 14, pp. 41-54, (2006).
    • (2006) Set-Valued Anal , vol.14 , pp. 41-54
    • Geoffroy, M.H.1    Hilout, S.2    Piétrus, A.3
  • 11
    • 0035533685 scopus 로고    scopus 로고
    • The Newton method for operators with Hölder continuous first derivative
    • M. A. Hernàndez, The Newton method for operators with Hölder continuous first derivative, J. Optim. Theory Appl., 109, pp. 631-648, (2001).
    • (2001) J. Optim. Theory Appl. , vol.109 , pp. 631-648
    • Hernàndez, M.A.1
  • 12
    • 0036681220 scopus 로고    scopus 로고
    • Semilocal convergence of the secant method under mild convergence conditions of differentiability
    • M. A. Hernàndez, M. J. Rubio, Semilocal convergence of the secant method under mild convergence conditions of differentiability, Comput. and Math. with Appl., 44, pp. 277-285, (2002).
    • (2002) Comput. and Math. with Appl. , vol.44 , pp. 277-285
    • Hernàndez, M.A.1    Rubio, M.J.2
  • 16
    • 33750091296 scopus 로고    scopus 로고
    • A semilocal convergence of a secant-type method for solving generalized equations
    • S. Hilout, A. Piétrus, A semilocal convergence of a secant-type method for solving generalized equations, Positivity, 10, pp. 673-700, (2006).
    • (2006) Positivity , vol.10 , pp. 673-700
    • Hilout, S.1    Piétrus, A.2
  • 17
    • 84966206068 scopus 로고
    • Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis
    • B. S. Mordukhovich, Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis, Trans. Amer. Math. Soc., 343, pp. 609-657, (1994).
    • (1994) Trans. Amer. Math. Soc. , vol.343 , pp. 609-657
    • Mordukhovich, B.S.1
  • 18
    • 0000056025 scopus 로고
    • Generalized equations and their solutions, part I: basic theory
    • S. M. Robinson, Generalized equations and their solutions, part I: basic theory, Math. Programming Study, 10, pp. 128-141, (1979).
    • (1979) Math. Programming Study , vol.10 , pp. 128-141
    • Robinson, S.M.1
  • 19
    • 0020165423 scopus 로고
    • Generalized equations and their solutions, part II: applications to nonlinear programming
    • S. M. Robinson, Generalized equations and their solutions, part II: applications to nonlinear programming, Math. Programming Study, 19, pp. 200-221, (1982).
    • (1982) Math. Programming Study , vol.19 , pp. 200-221
    • Robinson, S.M.1
  • 20
    • 0000676135 scopus 로고
    • Lipschitzian properties of multifunctions
    • R. T. Rockafellar, Lipschitzian properties of multifunctions, Nonlinear Analysis 9, pp. 867-885, (1984).
    • (1984) Nonlinear Analysis , vol.9 , pp. 867-885
    • Rockafellar, R.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.