Browsing by Author "Robdera, Mangatiana A."
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A concise approach to real analysis
Robdera, Mangatiana A. (Lulu, www.lulu.com, 20141007) 
Extensions of the Lusin's Theorem, the SeveriniEgorov's Theorem and the Riesz Subsequence Theorems
Robdera, Mangatiana A. (ScienceDomain International; www.sciencedomain.org, 20161014)We give extensions of the Lusin’s Theorem, the SeveriniEgorov’s Theorem, and the Riesz Subsequence Theorems to the setting of a nonadditive vector valued set functions and sequences of functions taking values in general ... 
More on equivalence properties of RadonNikodym property types and Complete Continuity property types
Robdera, Mangatiana A. (Pushpa Publishing House, www.pphmj.com, 201301)We study the equivalence property of the I and IILRadonNikodým property (resp. I and IILcomplete continuity property) types of Banach spaces. As a byproduct, we obtain a proof of the following: F. LustPicard’s ... 
A new general approach to vector valued stochastic integration
Robdera, Mangatiana A. (International Journal of Modeling and Optimization, www.ijmo.org, 201408)We use an extended theory of integral that generalizes the integration of vector valued functions with respect to nonnegative, monotonic,countably subadditive set functions, in order to introduce a new approach to stochastic ... 
On cartesian nets and fubinitonelli type theorem
Robdera, Mangatiana A. (International Journal of Applied Physics and Mathematics, http://www.ijapm.org/, 201704)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 ... 
On natural characterizations of tensor integrability
Robdera, Mangatiana A. (Science Domain International, http://www.sciencedomain.org/, 20150504)We revisit the deﬁnition of the tensor integrability introduced in [1], and prove some useful characterizations that provide a foundation for studying relevant properties to the integration theory. As applications, we ... 
On nonmetric covering lemmas and extended Lebesguedifferentiation theorem
Robdera, Mangatiana A. (Science Domain International;http://www.sciencedomain.org, 20150328)We give a nonmetric version of the Besicovitch Covering Lemma and an extension of the LebesgueDifferentiation Theorem into the setting of the integration theory of vector valued functions. 
On size function topology and fixed point theorems
Robdera, Mangatiana A. (International Scientific Publications and Consulting Services, http://www.ispacs.com/about.php, 201706)In this paper, we introduce and study a metriclike (nonnecessarily 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 ... 
On summable bases in Banach spaces
Robdera, Mangatiana A. (Science Domian International, www.sciencedomain.org, 20140624)We introduce the notion of summable bases that naturally generalizes the notion of unconditional sequence bases for Banach spaces. We shall be particularly interested in some classical results on sequences and series in ... 
On the differentiability of vector valued additive set functions
Robdera, Mangatiana A.; Kagiso, Dintle (Scientific Research, http://www.scirp.org, 201311)The LebesgueNikodým Theorem states that for a Lebesgue measure λ:Σ〖⊂2〗^Ω→[0,∞) an additive set function F:Σ→R which is λabsolutely continuous is the integral of a Lebegsue integrable a measurable function ... 
On the OrliczPettis theorem for integrals
Robdera, Mangatiana A. (Pushpa Publishing House, www.pphmj.com, 201010)In this note, we propose a more efficient approach to the definition of the integral of Banachvalued functions that enables us to give an improved version of the OrliczPettis theorem for integrals. 
On the Riesz representation theorem and integral operators
Robdera, Mangatiana A. (NISC (Pty) Ltd, http://www.nisc.co.za/, 20151214)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 ... 
On the subspace problem for Quasinormed spaces
Robdera, Mangatiana A. (ScienceDomain International; www.sciencedomain.org, 20160702)A definitive positive answer to the socalled proper subspace problem (a.k.a. the atomic space problem) for quasinormed spaces is given: every infinite dimensional quasinormed space has a proper closed infinitedimensional ... 
A unified approach to integration theory
Robdera, Mangatiana A. (International Journal of Applied Physics and Mathematics, www.ijapm.org/, 201901)We investigate the common features and the resemblance of the central parts of the different existing integration theories to obtain a more unified approach to the notion of integral. Our approach gives a presentation of ... 
Unified approach to vector valued integration
Robdera, Mangatiana A. (Pushpa Publishing House, www.pphmj.com, 201306)We introduce a natural and more flexible approach to the definition of vector valued integral that will completely forgo any measurability assumption, strengthen the existing various classical concepts of ...