Sizwe Gladwell Mabizela

Born: October 1962

place: Ladysmith, SOUTH AFRICA

M.Sc. at Fort Hare

Ph.D. (1991) Pennsylvania State University
thesis: Parametric Approximation; Advisor: Frank Deutsch

Senior Lecturer at Capetown Unversity in South Africa

personal or universal URL:

Research Interests

Approximation Theory: Particularly interested in parametric approximation. The set from which one approximates depends on some parameter which may or may not be related to the element that is being approximated. Typical examples include problems of best one-sided approximation, parametric spline approximation, approximation with interpolatory constraints, and copositive approximation. The stability of the best approximation operator associated with such problems is of practical interest. Equally important is the question of existence of continuous selections for the best approximation operator.

Selected publications

  1. Mabizela, Sizwe Characterization of best approximations in metric linear spaces. Sci. Math. Jpn. 57 (2003), no. 2, 233--240.
  2. Mabizela, Sizwe Uniform Hausdorff strong uniqueness and continuity of parametric projections. Nonlinear Funct. Anal. Appl. 7 (2002), no. 3, 465--472.
  3. Dragomir, S. S.; Mabizela, S. Some error estimates in the trapezoidal quadrature rule. Tamsui Oxf. J. Math. Sci. 16 (2000), no. 2, 259--272.
  4. Dragomir, Sever S.; Mabizela, Sizwe Functional inequalities and best approximation. Approx. Theory Appl. (N.S.) 14 (1998), no. 2, 90--98.
  5. Mabizela, S. Weak Chebyshev subspaces and continuous selections for parametric projections. Constr. Approx. 14 (1998), no. 2, 301--310.
  6. Mabizela, Sizwe Upper semicontinuity of parametric projections. Set-Valued Anal. 4 (1996), no. 4, 315--325.
  7. Deutsch, Frank; Mabizela, Sizwe Best interpolatory approximation in normed linear spaces. J. Approx. Theory 85 (1996), no. 3, 250--268.
  8. Deutsch, Frank; Li, Wu; Mabizela, Sizwe Helly extensions and best approximation. Parametric optimization and related topics, III (Güstrow, 1991), 107--120, Approx. Optim., 3, Lang, Frankfurt am Main, 1993.
  9. Mabizela, Sizwe Continuity of the one-sided best uniform approximation operator. Quaestiones Math. 16 (1993), no. 2, 157--165.
  10. Mabizela, S.; Zhong, J. On the best uniform $\epsilon$-interpolation operator. Numer. Funct. Anal. Optim. 14 (1993), no. 1-2, 117--124.
  11. Mabizela, Sizwe The relationship between Lipschitz extensions, best approximations, and continuous selections. Quaestiones Math. 14 (1991), no. 3, 261--268.
  12. Mabizela, Sizwe On bounded linear $2$-functionals. Math. Japon. 35 (1990), no. 1, 51--55.
  13. Mabizela, Sizwe A characterization of strictly convex linear $2$-normed spaces. Quaestiones Math. 12 (1989), no. 2, 201--204.

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