Dr. Sizwe G. Mabizela

Personal

Prefix: Dr.
First Name: Sizwe
Middle Name: G.
Last Name: Mabizela

Education

Degree: M.S.
Graduation Year: 1991
Major: Mathematics

Degree: Ph.D.
Graduation Year: 1991
Major: Mathematics

Summary

Dr. Sizwe Mabizela's research interests lie in Approximation Theory. He is 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 associated with such problems is of practical interest. Equally important is the question of existence of continuous selections for the best approximation operator.

Biography

Dr. Sizwe Mabizela was born in Ladysmith, South Africa.

He recieved his PhD, from Pennsylvania State University, with a thesis on Parametric Approximation; his advisor was Dr. Frank Deutsch.

Dr. Mabizela serves as a senior lecturer at Capetown University in South Africa.

Selected Publications

Mabizela, Sizwe Characterization of best approximations in metric linear spacesSci. Math. Jpn. 57 (2003), no. 2, 233--240.

Mabizela, Sizwe Uniform Hausdorff strong uniqueness and continuity of parametric projectionsNonlinear Funct. Anal. Appl. (2002), no. 3, 465--472.

Dragomir, S. S.; Mabizela, S. Some error estimates in the trapezoidal quadrature ruleTamsui Oxf. J. Math. Sci. 16 (2000), no. 2, 259--272.

Dragomir, Sever S.; Mabizela, Sizwe Functional inequalities and best approximationApprox. Theory Appl. (N.S.) 14 (1998), no. 2, 90--98.

Mabizela, S. Weak Chebyshev subspaces and continuous selections for parametric projectionsConstr. Approx. 14 (1998), no. 2, 301--310.

Mabizela, Sizwe Upper semicontinuity of parametric projectionsSet-Valued Anal. (1996), no. 4, 315--325.

Deutsch, Frank; Mabizela, Sizwe Best interpolatory approximation in normed linear spacesJ. Approx. Theory 85 (1996), no. 3, 250--268.

Deutsch, Frank; Li, Wu; Mabizela, Sizwe Helly extensions and best approximationParametric 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 operatorQuaestiones Math. 16 (1993), no. 2, 157--165.

Mabizela, S.; Zhong, J. On the best uniform $\epsilon$-interpolation operatorNumer. Funct. Anal. Optim. 14 (1993), no. 1-2, 117--124.

Mabizela, Sizwe The relationship between Lipschitz extensions, best approximations, and continuous selectionsQuaestiones Math. 14 (1991), no. 3, 261--268.

Mabizela, Sizwe On bounded linear $2$-functionalsMath. Japon. 35 (1990), no. 1, 51--55.

Mabizela, Sizwe A characterization of strictly convex linear $2$-normed spacesQuaestiones Math. 12 (1989), no. 2, 201--204.

Lifetime

Year Born: 1962