Giving to RU
Rhodes>Mathematics>Old sites content>Research>Functional Analysis

Functional Analysis

Members

  • Andrew L. Pinchuck

Regular research collaborators

  • Coenraad C. A. Labuschagne

  • Gunther Jaeger


Description

This is a relatively new research initiative and we would like to establish functional analysis and related topics as successful research areas in the department. The current focus of research is probabilistic limit spaces which has connections to classical functional analysis. Any potential postgraduate students should feel free to make contact if they share any interest in the research areas listed below or are involved in complimentary topics. For further information, you can make email contact: a.pinchuck@ru.ac.za


Research topics

  • Functional Analysis

  • Measure Theory

  • Generalized Topology

  • Limit Spaces

  • Probabilistic Limit groups

  • Probabilistic limit vector spaces

  • Approach spaces

Related courses at Rhodes

  • Linear Algebra (second year)

  • Real Analysis (third year)

  • Topology (Honours)

  • Functional Analysis (Honours)

  • Measure theory (Honours)


Publications

  • A.L. Pinchuck, G. Jaeger, On the Isomorphy of categories of probabilistic limit spaces under t-norms, submitted to Acta Mathematica Hungarica, October, 2012.

  • C.C.A. Labuschagne, A.L. Pinchuck, Doob's decomposition of fuzzy submartingales via ordered near vector spaces, Journal of nonlinear Analysis and Optimization, Volume 2, No. 1 (2011), 39--52.

  • C.C.A. Labuschagne, A.L. Pinchuck, Doob's decomposition of set-valued submartingales via ordered near vector spaces, Quaest. Math., 32 (2009), 247--264.

  • C. C. A. Labuschagne, A. L. Pinchuck and C. J. van Alten, A vector lattice version of Radstrom's embedding theorem, Quaest. Math., 30 (2007), no. 3, Pages 285--308.

  • C. C. A. Labuschagne, A. L. Pinchuck, The set of fuzzy points of a fuzzy vector lattice is not a vector lattice}, Fuzzy sets & Systems, Volume 157, no. 20 , 16 October 2006, Pages 2783--2785.


Conference proceedings

W. Kotze, A.L. Pinchuck, A fuzzy Hahn-Banach theorem, Proceedings 12th International Fuzzy Systems Association World Congress, IFSA 2007 Cancun, Mexico, June 2007, Proceedings, Springer Verlag (2007), 427--435.


Talks, presentations, reports etc

  • A. L. Pinchuck, The Second Asian Conference on Nonlinear Analysis and Optimization (NAO-Asia 2010), Phuket, Thailand, 9 - 12 September 2010.

Talk presented: Doob's decomposition of fuzzy submartingales via ordered near vector spaces.

  • A. L. Pinchuck, IFSA/EUSFLAT 2009, Lisbon, Portugal, 20 - 24 July 2009.

Talk presented: Convergence theorems for generalized random variables and martingales.

  • A. L. Pinchuck, 12th International Fuzzy Systems Assoc. World Congress, IFSA 2007 Cancun, Mexico 18 - 21 June 2007

Talk presented: A Fuzzy Hahn-Banach Theorem.

  • A. L. Pinchuck, South African Mathematical Society Annual Congress, Rhodes University 31 October - 2 November 2005

Talk presented: On fuzzy vector lattices.

Last Modified: Tue, 05 Mar 2013 09:44:14 SAST