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 DeutschSenior Lecturer at Capetown Unversity in South Africa

personal or universal URL:

http://www.mth.uct.ac.za/staff/mabizela.html

email: sizwe@maths.uct.ac.za

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

**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. 4, 315--325.- 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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