Monotone Approximation of Random Functions with Multivariate Domains in Respect of Lattice Semi-Norms

• Anastassiou, G.A.: (1985a) Miscellaneous sharp inequalities and Korovkin-type convergence theorems involving sequences of probability measures. J. Approx. Theory 44, 384–390.

  Article  MathSciNet  MATH  Google Scholar 

• Anastassiou, G.A.: (1985b) A study of positive linear operators by the method of moments, one-dimensional case. J. Approx. Theory 45, 247–270.

  Article  MathSciNet  MATH  Google Scholar 

• Anastassiou, G.A.: (1987) On the degree of weak convergence of a sequence of finite measures to the unit measure under convexity. J. Approx. Theory 51, 333–349.

  Article  MathSciNet  MATH  Google Scholar 

• Anastassiou, G.A.: (1989a) Smooth rate of weak convergence of convex type positive finite measures. J. Math. Anal. Appl. (to appear).

• Anastassiou, G.A.: (1989b) Rate of convergence of non-positive generalized convolution type operators. J. Math. Anal. Appl. (to appear).

• Berens, H., Lorentz, G.G.: (1973) Theorems of Korovkin type for positive linear operators on Banach lattices. In: Approximation theory (edited by G.G. Lorentz), 1–30. New York: Academic Press.

  Google Scholar 

• Cheney, E.W.: (1966) Introduction to approximation theory. New York: McGraw-Hill.

  MATH  Google Scholar 

• Censor, E.: (1971) Quantitative results for positive linear approximation operators. J. Approx. Theory 4, 442–450.

  Article  MathSciNet  MATH  Google Scholar 

• De Vore, R.A.: (1972) The approximation of continuous functions by positive linear operators. Lecture notes in mathematics, Vol. 293. Berlin, New York: Springer.

  Google Scholar 

• Ditzian, Z.: (1986)Inverse theorems for multidimensional Bernstein operators. Pacific J. Math. 121, 293–319.

  Article  MathSciNet  MATH  Google Scholar 

• Donner, K.: (1982)Extensions of positive operators and Korovkin theorems. Lecture notes in mathematics, Vol. 904. Berlin, New York: Springer.

  Google Scholar 

• Gonska, H.H.: (1983) On approximation of continuously differentiable functions by positive linear operators. Bull. Austral. Math. Soc. 27, 73–81.

  Article  MathSciNet  MATH  Google Scholar 

• Gonska, H.H., Meier-Gonska, J.: (1986) A bibliography on approximation of functions by Bernatein-type operators. In: Approximation Theory V (edited by C.K. Chui, L.L. Schumaker and J.D. Ward), 621–654. Orlando: Academic Press.

  Google Scholar 

• Hahn, L.: (1982) Stochastic methods in connections with approximation theorems for positive linear operators. Pacific J. Math. 101, 307–319.

  Article  MathSciNet  MATH  Google Scholar 

• Keimel, K., Roth, W.: (1988) A Korovkin type approximation theorem for set-valued functions. Proc. Amer. Math. Soc. 104, 819–823.

  Article  MathSciNet  MATH  Google Scholar 

• Keimel, K., Roth, W.: (1990) Ordered cones and approximation. Preprint, Department of Mathematics, University of Bahrain.

• Luxemburg, W.A.J., Zaanen, A.C.: (1971) Riesz spaces I. Amsterdam: North Holland.

• Mond, B., Vasudevan, R.: (1980) On approximation by linear positive operators. J. Approx. Theory 30, 334–336.

  Article  MathSciNet  Google Scholar 

• Nishishiraho, T.: (1982) Quantitative theorems on approximation processes of positive linear operators. In: Multivariate approximation theory II (edited by W. Schempp and K. Zeller), ISNM 61, 297-311. Basel, Boston, Stuttgart: Birkhäuser.

  Google Scholar 

• Roth, W.: (1989) Families of convex subsets and Korovkin type theorems in locally convex spaces. Rev. Roumaine Math. Pures et Appl. 34, 329–346.

  MATH  Google Scholar 

• Sablonnière, P.: (1988) Positive spline operators and orthogonal splines. J. Approx. Theory 52, 28–42.

  Article  MathSciNet  Google Scholar 

• Schaefer, H.H.: (1974) Banach lattices and positive operators. Berlin: Springer.

  Book  MATH  Google Scholar 

• Scheffold, E.: (1973) Ein allgemeiner Korovkin-Satz für lokalkonvexe Vektorverbände. Math. Z. 132, 209–214.

  Article  MathSciNet  MATH  Google Scholar 

• Schempp, W.: (1972) A note on Korovkin test families. Arch. Math. 23, 521–524.

  Article  MathSciNet  MATH  Google Scholar 

• Weba, M.: (1986) Korovkin systems of stochastic processes. Math. Z. 192, 73–80.

  Article  MathSciNet  MATH  Google Scholar 

• Weba, M.: (1989) Quantitative results on monotone approximation of stochastic processes. Probab. Math. Statist. (to appear).

• Weba, M.: (1990) A quantitative Korovkin theorem for random functions with multivariate domains. J. Approx. Theory 61, 74–87.

  Article  MathSciNet  MATH  Google Scholar 

• Wolff, M.: (1978) On the universal Korovkin closure of subsets in vector lattices. J. Approx. Theory 22, 243–253.

  Article  MathSciNet  MATH  Google Scholar 

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