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Detlef H. Mache    eMail: Detlef H. Mache

    Advanced Problems in Constructive Approximation
         (edited by M.D. Buhmann and D.H. Mache)
         Int. Series of Numerical Mathematics Vol. 142, (ISBN 3-7643-6648-6)
         Birkhäuser Verlag Basel (2003).

    New Developments in Approximations Theory
        (edited by M.D. Buhmann, M. Felten,  D.H. Mache and M.W. Müller)
        Int. Series of Numerical Mathematics Vol. 132, (ISBN 3-7643-6143-3) 
        Birkhäuser Verlag Basel (1999).

    Approximation Theory 
       (edited by M. Felten,  D.H. Mache and M.W. Müller)
       Mathematical Research, Vol. 86 (ISBN 3-05-501673-4), 
       Akademie Verlag Berlin (Wiley-Group) (1995).

    Journal (Editor)

     Journal General Mathematics (ISSN 1221 - 5023) · Electronic Edition 
 
 
 

      Publications (since 1991)

-     Finding relevant input Arguments with Radial Basisfunction Networks (jointly with Meyer, J.)
       preprint (2004)

-     Rekonstruktionsbasierte Selektion relevanter Einflussgrößen (jointly with Kiendl, H., Meyer, J., Schauten, D.)
       in: Computational Intelligence (Sonderforschungsbereich 531 „Design und Management komplexer technischer Prozesse
       & Systeme mit Methoden der Computational Intelligence“ ) ISSN 1433-3325   (2003)

-     The Rate of Approximation by Interpolating the Endpoints, 
      Primary publication: Technical Report (Institute Applied Mathematics), University Dortmund (2003).

-     Generalized Methods using Integral Transforms and Convolution Structures with Orthogonal Polynomials,
      in: Journal Rendiconti del Circolo Matematicodi Palermo, Serie II, Suppl. 68 (2002), 625 -640.
    

-    Approximation by Bernstein Quasi-Interpolants, (jointly with P. Mache);
      Primary publication: Technical Report Nr. 184 (Institute Applied Mathematics), University Dortmund (2000),
      in: Numerical Functional Analysis and Optimization Vol. 22 (1 & 2), (2001), 159 - 175.

-    (C,1) Means of Orthonormal Expansions for Exponential Weights,  (jointly with D.S. Lubinsky);
      Primary publication in: Graduiertenkolleg Mathematik im Bereich ihrer Wechselwirkung mit der Physik, Mathematisches 
      Institut, Ludwig-Maximilians Universität München, (1998),
      in: Journal of Approximation Theory, Vol. 103, No.1, (2000), 151 - 182.
 

-    Certain Results involving Gammaoperators, (jointly with A. Lupas, V. Maier, M.W. Müller);
      in:  Int. Series of Numerical Mathematics Vol. 132,  Birkhäuser Verlag Basel (1999), 199 - 214.

-    On Approximation Properties of Stancu-Kantorovich Operators, (jointly with B. Della Vecchia);
      in: Revue d'Analyse Numerique et de Theorie de l' Approximation, Tome 27, No. 1 (1998), 71 - 80.

-    Linear Combinations of Gammaoperators in $L_p$ - Spaces, (jointly with A. Lupas, V. Maier, M.W. Müller);
      in: Results in Mathematics 34 (1998), 156 - 168.

-    Optimale Konvergenzordnung positiver Summationsverfahren der Durrmeyer Operatoren mit Jacobi - 
      Gewichtungen;
    Habilitation thesis, Dortmund (1997).

-     On Numerical Differentiation, (jointly with A. Lupas);
      in: Revue d' Analyse Numerique et de Theorie de l' Approximation, Tome 26, No. 1-2 (1997), 109 - 115.

-     Approximation by $V_n$ - Operators, (jointly with A. Lupas);
      in: Facta Univ. Ser. Math. Inform. 12 (1997), 203 - 216.

-     Summation of Durrmeyer Operators with Chebyshev Weights;
      in: Approximation and Optimization, Proceedings of the Int.Conf. on Approximation and Optimization - ICAOR, 
      Cluj-Napoca Vol. I, (1996), 307 - 318.

-    Estimations of Chebyshev Convolution Operators by an Algebraic Modulus of Smoothness, (jointly with M. Felten);
      in: Numerical Functional Analysis and Optimization Vol. 17 (5 & 6), (1996), 577 - 585.

-     Characterization Theorems for the Approximation by a Family of Operators, (jointly with D.X. Zhou);
      in: Journal of Approximation Theory,  Vol. 84, No. 2, (1996), 145 - 161.

-    The $\Theta$ -- Transformation of Certain Positive Linear Operators,  (jointly with A. Lupas);
      in: International Journal of Mathematics and Mathematical Sciences, Vol. 19, No. 4, (1996), 667 - 678.

-    Weighted $L_p$ - Approximation of Derivatives by the Method of Gammaoperators, (jointly with A. Lupas, M.W. Müller);
      in: Results in Mathematics, Vol. 28, No. 3/4 (1995), 277 - 286.

-    A Link between Bernstein Polynomials and Durrmeyer Polynomials with Jacobi Weights;
      in: Approximation Theory  VIII, Vol. 1, Approximation and Interpolation, Charles K. Chui and Larry L. Schumaker (eds.),
      World Scientific Publishing Co., (1995), 403 - 410.

-     Generalization of Bernstein - Type Approximation Methods, (jointly with I. Gavrea);
      in: Approximation Theory, Proc. IDoMAT 95, Mathematical Research, Vol. 86, Akademie Verlag, Berlin, (1995), 115-- 126.

-    Best Direct and Converse Results for Lagrange - Type Operators, (jointly with D.X. Zhou);
      in: Approximation Theory and its Applications, Vol. 11, No. 2, (1995), 76 - 93.

-     Equivalence Theorem on Weighted Simultaneous $L_p$ -- Approximation by the Method of Kantorovic Operators;
      in: Journal of Approximation Theory, Vol. 78, No. 3, (1994), 321 - 350.

-    A Method for Summability of Lagrange Interpolation;
      in: International Journal of Mathematics and Mathematical Sciences, Vol. 17, No. 1, (1994), 19 - 26.

-    Approximation by Linear Positive Polynomial Operators with Saturation Order ${\cal O}(n^{-2})$;
      in:"Tiberiu Popoviciu " Seminaire Itinerant D'equations Fonctionnelles, Approximation et Convexite, Faculte
      de Mathematique, Universite Babes - Bolyai, Cluj - Napoca, Vol. 6, (1993), 115 - 122.

-    New local error estimates for Meyer - König and Zeller Kantorovic-operators using maximal functions, 
      (jointly with M.W. Müller);
      in: Mathematica (Cluj), Tome 34 (57), No. 2, (1992), 157 - 165.

-     Gewichtete Simultanapproximation in der $L_p$ - Metrik durch das Verfahren der Kantorovic Operatoren, 
      Dissertation, University of Dortmund (1991).