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Volumn 67, Issue 8, 2007, Pages 2361-2369

A generalization of the Banach contraction principle with high order of convergence of successive approximations

Author keywords

Fixed point theorems; Gauge functions; Iterative methods; Newton method; Semilocal convergence

Indexed keywords

DERIVATIVES; ITERATIVE METHODS; MATHEMATICAL MODELS; METRIC SYSTEM; NEWTON-RAPHSON METHOD;

EID: 34250743165     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.09.008     Document Type: Article
Times cited : (79)

References (20)
  • 1
    • 34250747666 scopus 로고
    • Contractors with nonlinear majorant functions and equations in Banach spaces
    • Altman M. Contractors with nonlinear majorant functions and equations in Banach spaces. Boll. Unione Mat. Ital. 9 (1974) 615-637
    • (1974) Boll. Unione Mat. Ital. , vol.9 , pp. 615-637
    • Altman, M.1
  • 3
    • 0009446755 scopus 로고
    • Generalized contractions and fixed-point theorems
    • Ćirić Lj. Generalized contractions and fixed-point theorems. Publ. Inst. Math. 12 (1971) 19-26
    • (1971) Publ. Inst. Math. , vol.12 , pp. 19-26
    • Ćirić, Lj.1
  • 4
    • 34250700230 scopus 로고
    • A certain fixed-point principle
    • (in Russian); Soviet Math. Dokl. 12 (1971) 813-816 (Engl. transl.)
    • Gel'man A. A certain fixed-point principle. Dokl. Akad. Nauk SSSR 198 (1971) 506-508 (in Russian); Soviet Math. Dokl. 12 (1971) 813-816 (Engl. transl.)
    • (1971) Dokl. Akad. Nauk SSSR , vol.198 , pp. 506-508
    • Gel'man, A.1
  • 5
    • 34250732575 scopus 로고
    • Another view of fixed point theory
    • Hicks T.L. Another view of fixed point theory. Math. Japonica 35 (1990) 231-234
    • (1990) Math. Japonica , vol.35 , pp. 231-234
    • Hicks, T.L.1
  • 6
    • 0001293657 scopus 로고
    • A Banach type fixed point theorem
    • Hicks T., and Rhoades B.E. A Banach type fixed point theorem. Math. Japonica 24 (1979) 327-330
    • (1979) Math. Japonica , vol.24 , pp. 327-330
    • Hicks, T.1    Rhoades, B.E.2
  • 7
    • 0037098597 scopus 로고    scopus 로고
    • On Newton's method under Hölder continuous derivative
    • Huang Z.D. On Newton's method under Hölder continuous derivative. J. Math. Anal. Appl. 270 (2002) 332-339
    • (2002) J. Math. Anal. Appl. , vol.270 , pp. 332-339
    • Huang, Z.D.1
  • 8
    • 0039699333 scopus 로고
    • Equivalent conditions and the Meir-Keeler type theorems
    • Jachymski J. Equivalent conditions and the Meir-Keeler type theorems. J. Math. Anal. Appl. 194 (1995) 293-303
    • (1995) J. Math. Anal. Appl. , vol.194 , pp. 293-303
    • Jachymski, J.1
  • 10
    • 1842867542 scopus 로고
    • Funktionalungleichungen und iterationsverfahren
    • Kornstaedt H.-J. Funktionalungleichungen und iterationsverfahren. Aequationes Math. 13 (1975) 21-45
    • (1975) Aequationes Math. , vol.13 , pp. 21-45
    • Kornstaedt, H.-J.1
  • 11
    • 0011728646 scopus 로고
    • Integrable solutions of functional equations
    • Matkowski J. Integrable solutions of functional equations. Dissertationes Math. 127 (1975)
    • (1975) Dissertationes Math. , vol.127
    • Matkowski, J.1
  • 12
    • 28844488424 scopus 로고
    • Fixed point theorems for contractive mappings in metric spaces
    • Matkowski J. Fixed point theorems for contractive mappings in metric spaces. Cas. Pest. Mat. 105 (1980) 341-344
    • (1980) Cas. Pest. Mat. , vol.105 , pp. 341-344
    • Matkowski, J.1
  • 13
    • 0000854252 scopus 로고
    • On the convergence of L.V. Kantorovic's method of solution of functional equations and its applications
    • (in Russian)
    • Mysovskih I.P. On the convergence of L.V. Kantorovic's method of solution of functional equations and its applications. Dokl. Acad. Nauk SSSR 70 (1950) 565-568 (in Russian)
    • (1950) Dokl. Acad. Nauk SSSR , vol.70 , pp. 565-568
    • Mysovskih, I.P.1
  • 15
    • 26844553864 scopus 로고
    • A unified approach to fixed points of contractive maps
    • Park S. A unified approach to fixed points of contractive maps. J. Korean Math. Soc. 16 (1980) 95-105
    • (1980) J. Korean Math. Soc. , vol.16 , pp. 95-105
    • Park, S.1
  • 16
    • 0006842410 scopus 로고
    • The rate of convergence of Newton's process
    • Ptak V. The rate of convergence of Newton's process. Numer. Math. 25 (1976) 279-285
    • (1976) Numer. Math. , vol.25 , pp. 279-285
    • Ptak, V.1
  • 17
    • 28844507797 scopus 로고    scopus 로고
    • Fixed point theorems in metric spaces
    • Proinov P.D. Fixed point theorems in metric spaces. Nonlinear Anal. 64 (2006) 546-557
    • (2006) Nonlinear Anal. , vol.64 , pp. 546-557
    • Proinov, P.D.1
  • 18
    • 0002214493 scopus 로고
    • A unified convergence theory for a class of iterative processes
    • Rheinboldt W.C. A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal. 5 (1968) 42-63
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 42-63
    • Rheinboldt, W.C.1
  • 19
    • 0000685483 scopus 로고
    • Newton's method under mild differentiability conditions with error analysis
    • Rokne J. Newton's method under mild differentiability conditions with error analysis. Numer. Math. 18 (1972) 401-412
    • (1972) Numer. Math. , vol.18 , pp. 401-412
    • Rokne, J.1
  • 20
    • 34250743881 scopus 로고    scopus 로고
    • I.A. Rus, Teoria Punctului Fix, II, Univ. Babes, Cluj, 1973


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.