Sizwe Gladwell Mabizela
Born: October 1962
place: Ladysmith, SOUTH AFRICA
M.Sc. at Fort
Ph.D. (1991) Pennsylvania
thesis: Parametric Approximation; Advisor: Frank Deutsch
at Capetown Unversity in South Africa
personal or universal URL: http://www.mth.uct.ac.za/staff/mabizela.html
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.
- Mabizela, Sizwe Characterization of best approximations
in metric linear spaces. Sci. Math. Jpn. 57 (2003),
no. 2, 233--240.
- Mabizela, Sizwe Uniform Hausdorff strong uniqueness
and continuity of parametric projections. Nonlinear Funct.
Anal. Appl. 7 (2002), no. 3, 465--472.
- Dragomir, S. S.; Mabizela, S. Some error estimates
in the trapezoidal quadrature rule. Tamsui Oxf. J. Math.
Sci. 16 (2000), no. 2, 259--272.
- Dragomir, Sever S.; Mabizela, Sizwe Functional
inequalities and best approximation. Approx. Theory Appl.
(N.S.) 14 (1998), no. 2, 90--98.
- Mabizela, S. Weak Chebyshev subspaces and continuous
selections for parametric projections. Constr. Approx.
14 (1998), no. 2, 301--310.
- Mabizela, Sizwe Upper semicontinuity of parametric
projections. Set-Valued Anal. 4 (1996), no.
- Deutsch, Frank; Mabizela, Sizwe Best interpolatory
approximation in normed linear spaces. J. Approx. Theory
85 (1996), no. 3, 250--268.
- 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.
- Mabizela, Sizwe Continuity of the one-sided best
uniform approximation operator. Quaestiones Math.
16 (1993), no. 2, 157--165.
- Mabizela, S.; Zhong, J. On the best uniform $\epsilon$-interpolation
operator. Numer. Funct. Anal. Optim. 14 (1993),
no. 1-2, 117--124.
- Mabizela, Sizwe The relationship between Lipschitz
extensions, best approximations, and continuous selections.
Quaestiones Math. 14 (1991), no. 3, 261--268.
- Mabizela, Sizwe On bounded linear $2$-functionals.
Math. Japon. 35 (1990), no. 1, 51--55.
- Mabizela, Sizwe A characterization of strictly
convex linear $2$-normed spaces. Quaestiones Math.
12 (1989), no. 2, 201--204.
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