메뉴 건너뛰기




Volumn 349, Issue 2, 2009, Pages 317-334

Convergence and rate of approximation for linear integral operators in BVφ-spaces in multidimensional setting

Author keywords

modulus of smoothness; Higher order of approximation; Linear convolution integral operators; Lipschitz classes; Multidimensional variation; Rate of approximation

Indexed keywords


EID: 53249130636     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.08.029     Document Type: Article
Times cited : (43)

References (38)
  • 1
    • 33750906082 scopus 로고    scopus 로고
    • Convergence in variation and rate of approximation for nonlinear integral operators of convolution type
    • Angeloni L., and Vinti G. Convergence in variation and rate of approximation for nonlinear integral operators of convolution type. Results Math. 49 1-2 (2006) 1-23
    • (2006) Results Math. , vol.49 , Issue.1-2 , pp. 1-23
    • Angeloni, L.1    Vinti, G.2
  • 2
    • 53249145747 scopus 로고    scopus 로고
    • Approximation by means of nonlinear integral operators in the space of functions with bounded φ-variation
    • Angeloni L., and Vinti G. Approximation by means of nonlinear integral operators in the space of functions with bounded φ-variation. Differential Integral Equations 20 3 (2007) 339-360
    • (2007) Differential Integral Equations , vol.20 , Issue.3 , pp. 339-360
    • Angeloni, L.1    Vinti, G.2
  • 3
    • 53249109863 scopus 로고
    • Alcuni teoremi di convergenza per l'integrale multiplo del Calcolo delle Variazioni
    • Bardaro C. Alcuni teoremi di convergenza per l'integrale multiplo del Calcolo delle Variazioni. Atti Semin. Mat. Fis. Univ. Modena 31 (1982) 302-324
    • (1982) Atti Semin. Mat. Fis. Univ. Modena , vol.31 , pp. 302-324
    • Bardaro, C.1
  • 4
    • 29944433767 scopus 로고    scopus 로고
    • Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals
    • Bardaro C., Butzer P.L., Stens R.L., and Vinti G. Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals. Analysis 23 (2003) 299-340
    • (2003) Analysis , vol.23 , pp. 299-340
    • Bardaro, C.1    Butzer, P.L.2    Stens, R.L.3    Vinti, G.4
  • 8
    • 53249088358 scopus 로고
    • Sull'approssimazione dell'integrale multiplo del Calcolo delle Variazioni
    • Boni M. Sull'approssimazione dell'integrale multiplo del Calcolo delle Variazioni. Atti Semin. Mat. Fis. Univ. Modena 20 1 (1971) 187-211
    • (1971) Atti Semin. Mat. Fis. Univ. Modena , vol.20 , Issue.1 , pp. 187-211
    • Boni, M.1
  • 10
    • 0000923872 scopus 로고
    • Sulle funzioni a variazione limitata
    • Cesari L. Sulle funzioni a variazione limitata. Ann. Sc. Norm. Super. Pisa 5 (1936) 299-313
    • (1936) Ann. Sc. Norm. Super. Pisa , vol.5 , pp. 299-313
    • Cesari, L.1
  • 11
    • 0032050010 scopus 로고    scopus 로고
    • Mappings of bounded Φ-variation with arbitrary function Φ
    • Chistyakov V.V., and Galkin O.E. Mappings of bounded Φ-variation with arbitrary function Φ. J. Dyn. Control Syst. 4 2 (1998) 217-247
    • (1998) J. Dyn. Control Syst. , vol.4 , Issue.2 , pp. 217-247
    • Chistyakov, V.V.1    Galkin, O.E.2
  • 12
    • 0000245505 scopus 로고
    • Su una teoria generale della misura (r - 1)-dimensionale in uno spazio ad r dimensioni
    • De Giorgi E. Su una teoria generale della misura (r - 1)-dimensionale in uno spazio ad r dimensioni. Ann. Mat. Pura Appl. 36 4 (1954) 191-213
    • (1954) Ann. Mat. Pura Appl. , vol.36 , Issue.4 , pp. 191-213
    • De Giorgi, E.1
  • 13
    • 0003343498 scopus 로고
    • Minimal Surfaces and Functions of Bounded Variation
    • Birkhäuser-Verlag, Basel
    • Giusti E. Minimal Surfaces and Functions of Bounded Variation. Monogr. Math. vol. 80 (1984), Birkhäuser-Verlag, Basel
    • (1984) Monogr. Math. , vol.80
    • Giusti, E.1
  • 14
    • 84972542010 scopus 로고
    • Sublinear functions of measures and variational integrals
    • Goffman C., and Serrin J. Sublinear functions of measures and variational integrals. Duke Math. J. 31 1 (1964) 159-178
    • (1964) Duke Math. J. , vol.31 , Issue.1 , pp. 159-178
    • Goffman, C.1    Serrin, J.2
  • 15
    • 53249149608 scopus 로고
    • Modular spaces of generalized variation
    • Herda H.H. Modular spaces of generalized variation. Studia Math. 30 (1968) 21-42
    • (1968) Studia Math. , vol.30 , pp. 21-42
    • Herda, H.H.1
  • 17
    • 0001048449 scopus 로고
    • Sur la serie de Fourier
    • Jordan C. Sur la serie de Fourier. C. R. Acad. Sci. Paris 92 (1881) 228-230
    • (1881) C. R. Acad. Sci. Paris , vol.92 , pp. 228-230
    • Jordan, C.1
  • 18
    • 84972833400 scopus 로고
    • On constructive one-sided approximation of multivariate functions of bounded variation
    • Lenze B. On constructive one-sided approximation of multivariate functions of bounded variation. Numer. Funct. Anal. Optim. 11 1-2 (1990) 55-83
    • (1990) Numer. Funct. Anal. Optim. , vol.11 , Issue.1-2 , pp. 55-83
    • Lenze, B.1
  • 19
    • 51849184170 scopus 로고
    • A hyperbolic modulus of smoothness for multivariate functions of bounded variation
    • Lenze B. A hyperbolic modulus of smoothness for multivariate functions of bounded variation. Approx. Theory Appl. 7 1 (1991) 1-15
    • (1991) Approx. Theory Appl. , vol.7 , Issue.1 , pp. 1-15
    • Lenze, B.1
  • 20
    • 0346125681 scopus 로고
    • Sur une classe de fonctionnelles linéaires
    • Love E.R., and Young L.C. Sur une classe de fonctionnelles linéaires. Fund. Math. 28 (1937) 243-257
    • (1937) Fund. Math. , vol.28 , pp. 243-257
    • Love, E.R.1    Young, L.C.2
  • 21
    • 0013097619 scopus 로고
    • On some properties of functions of generalized variation
    • Maligranda L., and Orlicz W. On some properties of functions of generalized variation. Monatsh. Math. 104 (1987) 53-65
    • (1987) Monatsh. Math. , vol.104 , pp. 53-65
    • Maligranda, L.1    Orlicz, W.2
  • 22
    • 33750925753 scopus 로고    scopus 로고
    • Φ-variation and nonlinear integral operators
    • (special issue of the International Conference in Honour of Prof. Calogero Vinti)
    • Mantellini I., and Vinti G. Φ-variation and nonlinear integral operators. Atti Semin. Mat. Fis. Univ. Modena 46 Suppl. (1998) 847-862 (special issue of the International Conference in Honour of Prof. Calogero Vinti)
    • (1998) Atti Semin. Mat. Fis. Univ. Modena , vol.46 , Issue.SUPPL , pp. 847-862
    • Mantellini, I.1    Vinti, G.2
  • 24
    • 0003311060 scopus 로고
    • Orlicz Spaces and Modular Spaces
    • Springer-Verlag
    • Musielak J. Orlicz Spaces and Modular Spaces. Lecture Notes in Math. vol. 1034 (1983), Springer-Verlag
    • (1983) Lecture Notes in Math. , vol.1034
    • Musielak, J.1
  • 25
    • 0042200370 scopus 로고
    • Nonlinear approximation in some modular function spaces I
    • Musielak J. Nonlinear approximation in some modular function spaces I. Math. Japonica 38 (1993) 83-90
    • (1993) Math. Japonica , vol.38 , pp. 83-90
    • Musielak, J.1
  • 26
    • 0001845851 scopus 로고
    • On generalized variations (I)
    • Musielak J., and Orlicz W. On generalized variations (I). Studia Math. 18 (1959) 11-41
    • (1959) Studia Math. , vol.18 , pp. 11-41
    • Musielak, J.1    Orlicz, W.2
  • 27
    • 34249769183 scopus 로고
    • On approximation of functions in terms of Φ-variation
    • Ramazanov A.R.K. On approximation of functions in terms of Φ-variation. Anal. Math. 20 (1994) 263-281
    • (1994) Anal. Math. , vol.20 , pp. 263-281
    • Ramazanov, A.R.K.1
  • 30
    • 33750908784 scopus 로고    scopus 로고
    • φ (R) for a class of nonlinear Volterra-Hammerstein integral operators and applications
    • φ (R) for a class of nonlinear Volterra-Hammerstein integral operators and applications. J. Concr. Appl. Anal. 1 4 (2003) 287-306
    • (2003) J. Concr. Appl. Anal. , vol.1 , Issue.4 , pp. 287-306
    • Sciamannini, S.1    Vinti, G.2
  • 31
    • 10044291101 scopus 로고
    • On the differentiability of functions of several variables
    • Serrin J. On the differentiability of functions of several variables. Arch. Ration. Mech. Anal. 7 (1961) 359-372
    • (1961) Arch. Ration. Mech. Anal. , vol.7 , pp. 359-372
    • Serrin, J.1
  • 32
    • 0000333677 scopus 로고
    • On the definition and properties of certain variational integrals
    • Serrin J. On the definition and properties of certain variational integrals. Trans. Amer. Math. Soc. 101 (1961) 139-167
    • (1961) Trans. Amer. Math. Soc. , vol.101 , pp. 139-167
    • Serrin, J.1
  • 33
    • 53249111792 scopus 로고
    • On convergence of singular integrals in the generalized variation metric
    • Szelmeczka J. On convergence of singular integrals in the generalized variation metric. Funct. Approx. Comment. Math. 15 (1986) 53-58
    • (1986) Funct. Approx. Comment. Math. , vol.15 , pp. 53-58
    • Szelmeczka, J.1
  • 34
    • 33750921310 scopus 로고
    • Su alcuni concetti dell'analisi moderna
    • Tonelli L. Su alcuni concetti dell'analisi moderna. Ann. Sc. Norm. Super. Pisa 11 2 (1942) 107-118
    • (1942) Ann. Sc. Norm. Super. Pisa , vol.11 , Issue.2 , pp. 107-118
    • Tonelli, L.1
  • 35
    • 33750918532 scopus 로고
    • Perimetro-variazione
    • Vinti C. Perimetro-variazione. Ann. Sc. Norm. Super. Pisa 18 3 (1964) 201-231
    • (1964) Ann. Sc. Norm. Super. Pisa , vol.18 , Issue.3 , pp. 201-231
    • Vinti, C.1
  • 36
    • 85171984491 scopus 로고
    • The quadratic variation of a function and its Fourier coefficients
    • Wiener N. The quadratic variation of a function and its Fourier coefficients. Massachusetts J. Math. 3 (1924) 72-94
    • (1924) Massachusetts J. Math. , vol.3 , pp. 72-94
    • Wiener, N.1
  • 37
    • 0000821514 scopus 로고
    • An inequality of the Hölder type, connected with Stieltjes integration
    • Young L.C. An inequality of the Hölder type, connected with Stieltjes integration. Acta Math. 67 (1936) 251-282
    • (1936) Acta Math. , vol.67 , pp. 251-282
    • Young, L.C.1
  • 38
    • 0001018757 scopus 로고
    • i e m e bornée au sens de M. Wiener, et sur la convergence des séries de Fourier
    • i e m e bornée au sens de M. Wiener, et sur la convergence des séries de Fourier. C. R. Acad. Sci. Paris 204 (1937) 470-472
    • (1937) C. R. Acad. Sci. Paris , vol.204 , pp. 470-472
    • Young, L.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.