Research articles (Dept of Mathematics)http://hdl.handle.net/10311/632018-09-21T16:13:28Z2018-09-21T16:13:28ZOn the Riesz representation theorem and integral operatorsRobdera, Mangatiana A.http://hdl.handle.net/10311/17702017-11-25T00:01:17Z2015-12-14T00:00:00ZOn the Riesz representation theorem and integral operators
Robdera, Mangatiana A.
We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions.
2015-12-14T00:00:00ZFundamental Theorem of Calculus in Topological Vector SpacesRobdera, M. A.Kagiso, D. N.http://hdl.handle.net/10311/17662017-11-24T00:01:32Z2017-10-01T00:00:00ZFundamental Theorem of Calculus in Topological Vector Spaces
Robdera, M. A.; Kagiso, D. N.
We extend the notions of integration and differentiation to cover the class of functions taking values in topological vector spaces. We give versions of the Lebesgue-Nikodym Theorem and the Fundamental Theorem of Calculus in such a more general setting.
2017-10-01T00:00:00ZOn cartesian nets and fubini-tonelli type theoremRobdera, Mangatiana A.http://hdl.handle.net/10311/17132017-08-11T00:02:26Z2017-04-01T00:00:00ZOn cartesian nets and fubini-tonelli type theorem
Robdera, Mangatiana A.
The notion of Cartesian net is introduced in order to provide an appropriate setting for the notion of double limit for directed functions defined on Cartesian products of spaces. As an application, we obtain extensions of the Fubini-Tonelli type theorem to the setting of the extended notion of integrability recently introduced.
Original research paper
2017-04-01T00:00:00ZOn size function topology and fixed point theoremsRobdera, Mangatiana A.http://hdl.handle.net/10311/17122017-08-11T00:02:19Z2017-06-01T00:00:00ZOn size function topology and fixed point theorems
Robdera, Mangatiana A.
In this paper, we introduce and study a metric-like (non-necessarily metric) topology that is weaker than the original topology of a given topological space. The results are used to provide more useful and more general versions of some of the classical fixed point theorems.
2017-06-01T00:00:00Z