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Volumn 21, Issue 2, 2014, Pages 45-74

A unified approach for the convergence of nonlinear Kantorovich type operators

Author keywords

Estimates; Haar measure; Locally compact topological groups; Modular convergence; Nonlinear Kantorovich convolution type operators; Nonlinear Kantorovich Mellin type operators; Nonlinear Kantorovich sampling type operators; Orlicz spaces; Pointwise convergence; Uniform convergence

Indexed keywords


EID: 84974715527     PISSN: 1074133X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (7)

References (54)
  • 1
    • 33750926695 scopus 로고    scopus 로고
    • Rate of approximation for nonlinear integral operators with applications to signal processing
    • L. Angeloni, G. Vinti, Rate of approximation for nonlinear integral operators with applications to signal processing, Differential and Integral Equations 18 No. 8 (2005), 855-890.
    • (2005) Differential and Integral Equations , vol.18 , Issue.8 , pp. 855-890
    • Angeloni, L.1    Vinti, G.2
  • 3
    • 29944441495 scopus 로고    scopus 로고
    • Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals
    • C. Bardaro, P. L. Butzer, R. L. Stens, G. Vinti, Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals, J. Math. Anal. Appl. 316 No. 1 (2006), 269-306.
    • (2006) J. Math. Anal. Appl , vol.316 , Issue.1 , pp. 269-306
    • Bardaro, C.1    Butzer, P.L.2    Stens, R.L.3    Vinti, G.4
  • 5
    • 73849099362 scopus 로고    scopus 로고
    • Prediction by samples from the past with error estimates covering discontinuous signals
    • C. Bardaro, P. L. Butzer, R. L. Stens, G. Vinti, Prediction by samples from the past with error estimates covering discontinuous signals, IEEE Transactions on Information Theory 56 No. 1 (2010), 614-633.
    • (2010) IEEE Transactions on Information Theory , vol.56 , Issue.1 , pp. 614-633
    • Bardaro, C.1    Butzer, P.L.2    Stens, R.L.3    Vinti, G.4
  • 6
    • 27844463218 scopus 로고    scopus 로고
    • A modular convergence theorem for general nonlinear integral operators
    • C. Bardaro and I. Mantellini, A modular convergence theorem for general nonlinear integral operators, Comment. Math. 36 (1996), 27-37.
    • (1996) Comment. Math , vol.36 , pp. 27-37
    • Bardaro, C.1    Mantellini, I.2
  • 7
    • 84886639204 scopus 로고    scopus 로고
    • On linear combinations of multivariate generalized sampling type series
    • C. Bardaro and I. Mantellini, On linear combinations of multivariate generalized sampling type series, Mediterr. J. Math. 10 (2013), 1833-1852.
    • (2013) Mediterr. J. Math , vol.10 , pp. 1833-1852
    • Bardaro, C.1    Mantellini, I.2
  • 9
    • 0345807479 scopus 로고    scopus 로고
    • Approximation by nonlinear integral operators in some function spaces
    • C.Bardaro, J. Musielak, G. Vinti, Approximation by nonlinear integral operators in some function spaces, Ann. Polon. Math. 63 No. 2 (1996), 173-182.
    • (1996) Ann. Polon. Math , vol.63 , Issue.2 , pp. 173-182
    • Bardaro, C.1    Musielak, J.2    Vinti, G.3
  • 10
    • 70449517216 scopus 로고    scopus 로고
    • Nonlinear operators of integral type in some function spaces
    • C. Bardaro, J. Musielak, G. Vinti, Nonlinear operators of integral type in some function spaces, Collectanea Mathematica 48 (1997), 409-422.
    • (1997) Collectanea Mathematica , vol.48 , pp. 409-422
    • Bardaro, C.1    Musielak, J.2    Vinti, G.3
  • 12
    • 27844444162 scopus 로고    scopus 로고
    • An abstract approach to sampling type operators inspired by the work of P.L. Butzer. Part II-Nonlinear operators
    • C. Bardaro, G. Vinti, An abstract approach to sampling type operators inspired by the work of P.L. Butzer. Part II-Nonlinear operators, Sampling Theory in Signal and Image Processing 3 No. 1 (2004), 29-44.
    • (2004) Sampling Theory in Signal and Image Processing , vol.3 , Issue.1 , pp. 29-44
    • Bardaro, C.1    Vinti, G.2
  • 14
    • 84903472025 scopus 로고    scopus 로고
    • Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes
    • A. Boccuto, D. Candeloro, A.R. Sambucini, Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes, in print in Journal of Mathematical Analysis and Applications (2014).
    • (2014) Journal of Mathematical Analysis and Applications
    • Boccuto, A.1    Candeloro, D.2    Sambucini, A.R.3
  • 16
    • 0001114755 scopus 로고
    • A survey of the Whittaker-Shannon sampling theorem and some of its extentions
    • P.L. Butzer, A survey of the Whittaker-Shannon sampling theorem and some of its extentions, J. Math. Res. Exposition 3 (1983), 185-212.
    • (1983) J. Math. Res. Exposition , vol.3 , pp. 185-212
    • Butzer, P.L.1
  • 17
    • 0022699123 scopus 로고
    • The Shannon sampling series and the reconstruction of signals in terms of linear quadratic and cubic splines
    • P.L. Butzer, W. Engels, S. Ries, R.L. Stens, The Shannon sampling series and the reconstruction of signals in terms of linear, quadratic and cubic splines, SIAM J. Appl. Math. 46 No.2 (1986), 299-323.
    • (1986) SIAM J. Appl. Math , vol.46 , Issue.2 , pp. 299-323
    • Butzer, P.L.1    Engels, W.2    Ries, S.3    Stens, R.L.4
  • 18
    • 0010923391 scopus 로고
    • Generalized sampling approximation of multivariate signals:theory and applications
    • P.L. Butzer, A. Fisher, R.L. Stens, Generalized sampling approximation of multivariate signals:theory and applications, Note di Matematica 10 Suppl. No. 1 (1990), 173-191.
    • (1990) Note di Matematica , vol.10 , pp. 173-191
    • Butzer, P.L.1    Fisher, A.2    Stens, R.L.3
  • 21
    • 3042531131 scopus 로고    scopus 로고
    • An introduction to sampling analysis
    • F. Marvasti, Ed. Kluwer/Plenum, New York
    • P.L. Butzer, G. Schmeisser, R.L. Stens, An introduction to sampling analysis, In: Nonuniform sampling, F. Marvasti, Ed. Kluwer/Plenum, New York (2001), 17-121.
    • (2001) Nonuniform sampling , pp. 17-121
    • Butzer, P.L.1    Schmeisser, G.2    Stens, R.L.3
  • 22
    • 0017493091 scopus 로고
    • A sampling theorem for duration-limited functions with error estimates
    • P.L. Butzer, W. Splettstößer, A sampling theorem for duration-limited functions with error estimates, Information and Control 34 No. 1 (1977), 55-65.
    • (1977) Information and Control , vol.34 , Issue.1 , pp. 55-65
    • Butzer, P.L.1    Splettstößer, W.2
  • 23
    • 0002038798 scopus 로고
    • The sampling theorem and linear prediction in signal analysis Jahresber
    • P.L. Butzer, W. Splettstößer, R.L. Stens, The sampling theorem and linear prediction in signal analysis, Jahresber.Deutsch. Math.-Verein. 90 (1988), 1-70.
    • (1988) Deutsch. Math.-Verein , vol.90 , pp. 1-70
    • Butzer, P.L.1    Splettstößer, W.2    Stens, R.L.3
  • 24
    • 0026838009 scopus 로고
    • Sampling theory for not necessarily band-limited functions: A historical overview
    • P.L. Butzer, R.L. Stens, Sampling theory for not necessarily band-limited functions: a historical overview, SIAM Review 34 (1992), 40-53.
    • (1992) SIAM Review , vol.34 , pp. 40-53
    • Butzer, P.L.1    Stens, R.L.2
  • 26
    • 38649107028 scopus 로고    scopus 로고
    • Reconstruction of signals in lp(r)-space by generalized sampling series based on linear combinations of b-splines integral transforms
    • P.L. Butzer, R.L. Stens, Reconstruction of signals in Lp(R)-space by generalized sampling series based on linear combinations of B-splines, Integral Transforms Spec. Funct. 19 No. 1-2 (2008), 35-58.
    • (2008) Spec. Funct , vol.19 , Issue.1-2 , pp. 35-58
    • Butzer, P.L.1    Stens, R.L.2
  • 28
    • 84880406518 scopus 로고    scopus 로고
    • Approximation by nonlinear multivariate generalized sampling kantorovich operators and applications to image processing
    • D. Costarelli, G. Vinti, Approximation by nonlinear multivariate generalized sampling Kantorovich operators and applications to Image Processing, Numerical Function Analysis and Optimization 34 No. 8 (2013), 819-844.
    • (2013) Numerical Function Analysis and Optimization , vol.34 , Issue.8 , pp. 819-844
    • Costarelli, D.1    Vinti, G.2
  • 31
    • 0001204748 scopus 로고
    • Two limiting cases of Sobolev imbeddings
    • D.E. Edmunds, M.Krbec, Two limiting cases of Sobolev imbeddings, Houston J. Math. 21 No.1 (1995), 119-128.
    • (1995) Houston J. Math , vol.21 , Issue.1 , pp. 119-128
    • Edmunds, D.E.1    Krbec, M.2
  • 34
    • 0142087806 scopus 로고    scopus 로고
    • A sharp form of an embedding into exponential and double exponential spaces
    • S. Hencl, A sharp form of an embedding into exponential and double exponential spaces, J. Funct. Anal. 204 No. 1 (2003), 196-227.
    • (2003) J. Funct. Anal , vol.204 , Issue.1 , pp. 196-227
    • Hencl, S.1
  • 36
    • 0017558676 scopus 로고
    • Shannon sampling theorem-Its various extensions and applications: A tutorial review
    • A.J. Jerri, Shannon sampling theorem-Its various extensions and applications: A tutorial review, Proceedings of the IEEE, 65 No. 11 (1977), 1565-1596.
    • (1977) Proceedings of the IEEE , vol.65 , Issue.11 , pp. 1565-1596
    • Jerri, A.J.1
  • 38
    • 0347699499 scopus 로고    scopus 로고
    • Modular estimates for nonlinear integral operators and applications in fractional calculus
    • I. Mantellini, G. Vinti, Modular estimates for nonlinear integral operators and applications in fractional calculus, Numer. Funct. Anal. and Optimiz. 17 No. 1 & 3 (1996), 143-165.
    • (1996) Numer. Funct. Anal. and Optimiz , vol.17 , Issue.1-3 , pp. 143-165
    • Mantellini, I.1    Vinti, G.2
  • 39
    • 27844556091 scopus 로고    scopus 로고
    • Approximation results for nonlinear integral operators in modular spaces and applications
    • I. Mantellini, G. Vinti, Approximation results for nonlinear integral operators in modular spaces and applications, Annales Polonici Mathematici 81 No. 1 (2003), 55-71.
    • (2003) Annales Polonici Mathematici , vol.81 , Issue.1 , pp. 55-71
    • Mantellini, I.1    Vinti, G.2
  • 41
    • 0003311060 scopus 로고
    • Orlicz spaces and modular spaces
    • Springer-Verlag, Berlin
    • J. Musielak, Orlicz spaces and modular spaces, Lectures Notes in Mathematics, vol. 1034, Springer-Verlag, Berlin 1983.
    • (1983) Lectures Notes in Mathematics , vol.1034
    • Musielak, J.1
  • 46
    • 0010797227 scopus 로고
    • Approximation by generalized sampling series
    • Bl. Sendov, P. Petrushev, R. Maleev, S. Tashev (Eds.) 1984, Publishing House of the Bulgarian Academy of Sciences Sofia
    • S. Ries, R.L.Stens, Approximation by generalized sampling series, in: Bl. Sendov, P. Petrushev, R. Maleev, S. Tashev (Eds.), Constructive Theory of functions, in Proc. Conf., Varna, Bulgaria, 1984, Publishing House of the Bulgarian Academy of Sciences Sofia (1984), 746-756.
    • (1984) Constructive Theory of Functions, in Proc. Conf., Varna, Bulgaria , pp. 746-756
    • Ries, S.1    Stens, R.L.2
  • 48
    • 0002540844 scopus 로고
    • Note on the class Llog L
    • E.M. Stein, Note on the class Llog L, Studia Math. 32 (1969), 305-310.
    • (1969) Studia Math , vol.32 , pp. 305-310
    • Stein, E.M.1
  • 49
    • 0019004142 scopus 로고
    • Approximation to duration-limited functions by sampling sums
    • R. L. Stens, Approximation to duration-limited functions by sampling sums, Signal Process. 2 No. 2 (1980), 173-176.
    • (1980) Signal Process , vol.2 , Issue.2 , pp. 173-176
    • Stens, R.L.1
  • 50
    • 27844511616 scopus 로고    scopus 로고
    • A general approximation result for nonlinear integral operators and applications to signal processing
    • G. Vinti, A general approximation result for nonlinear integral operators and applications to signal processing, Applicable Analysis 79 (2001), 217-238.
    • (2001) Applicable Analysis , vol.79 , pp. 217-238
    • Vinti, G.1
  • 52
    • 70449519405 scopus 로고    scopus 로고
    • Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces
    • G. Vinti, L. Zampogni, Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces, Journal of Approximation Theory 161 (2009), 511-528.
    • (2009) Journal of Approximation Theory , vol.161 , pp. 511-528
    • Vinti, G.1    Zampogni, L.2
  • 53
    • 84874638760 scopus 로고    scopus 로고
    • A unifying approach to convergence of linear sampling type operators in Orlicz spaces
    • G. Vinti, L. Zampogni, A unifying approach to convergence of linear sampling type operators in Orlicz spaces, Advances in Differential Equations, 16 (2011), 573-600.
    • (2011) Advances in Differential Equations , vol.16 , pp. 573-600
    • Vinti, G.1    Zampogni, L.2
  • 54
    • 84910058049 scopus 로고    scopus 로고
    • Approximation results for a general class of Kantorovich type operators
    • G. Vinti, L. Zampogni, Approximation results for a general class of Kantorovich type operators, in print in Advanced Nonlinear Studies (2014).
    • (2014) Advanced Nonlinear Studies
    • Vinti, G.1    Zampogni, L.2


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