Masters Degrees (Pure Mathematics)https://researchspace.ukzn.ac.za/handle/10413/71212019-12-15T01:16:10Z2019-12-15T01:16:10ZOn amenability properties of some closed ideals of B(X)https://researchspace.ukzn.ac.za/handle/10413/163202019-06-13T01:01:55Z2018-01-01T00:00:00ZOn amenability properties of some closed ideals of B(X)
Abstract available in PDF file.
Master of Science in Mathematics. University of KwaZulu-Natal, Durban, 2018.
2018-01-01T00:00:00ZOn the geometry of CR-manifolds.https://researchspace.ukzn.ac.za/handle/10413/159142018-12-13T01:00:37Z2015-01-01T00:00:00ZOn the geometry of CR-manifolds.
We study two classes of CR-submanifolds in Kählerian and cosymplectic
manifolds. More precisely, we compare the geometry of CR-submanifolds of
the above two underlying smooth manifolds. We derive expressions relat-
ing the sectional curvatures, the necessary and sufficient conditions for the
integrability of distributions. Further, we study totally umbilical, totally
geodesic and foliation geometry of the CR-submanifolds of both spaces and
found many interesting results. We prove that, under some condition, there
are classes CR submanifold in cosymplectic space forms which are in the
classes extrinsic spheres. Examples are given throughout the thesis.
Master of Science in Mathematics. University of KwaZulu-Natal, Durban 2015.
2015-01-01T00:00:00ZIterative algorithms for approximating solutions of variational inequality problems and monotone inclusion problems.https://researchspace.ukzn.ac.za/handle/10413/158452018-11-17T01:00:36Z2017-01-01T00:00:00ZIterative algorithms for approximating solutions of variational inequality problems and monotone inclusion problems.
In this work, we introduce and study an iterative algorithm independent of the operator
norm for approximating a common solution of split equality variational inequality prob-
lem and split equality xed point problem. Using our algorithm, we state and prove a
strong convergence theorem for approximating an element in the intersection of the set
of solutions of a split equality variational inequality problem and the set of solutions of
a split equality xed point problem for demicontractive mappings in real Hilbert spaces.
We then considered nite families of split equality variational inequality problems and
proposed an iterative algorithm for approximating a common solution of this problem and
the multiple-sets split equality xed point problem for countable families of multivalued
type-one demicontractive-type mappings in real Hilbert spaces. A strong convergence re-
sult of the sequence generated by our proposed algorithm to a solution of this problem was
also established. We further extend our study from the frame work of real Hilbert spaces
to more general p-uniformly convex Banach spaces which are also uniformly smooth. In
this space, we introduce an iterative algorithm and prove a strong convergence theorem for
approximating a common solution of split equality monotone inclusion problem and split
equality xed point problem for right Bregman strongly nonexpansive mappings. Finally,
we presented numerical examples of our theorems and applied our results to study the
convex minimization problems and equilibrium problems.
Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban, 2017.
2017-01-01T00:00:00ZSome amenability properties on segal algebras.https://researchspace.ukzn.ac.za/handle/10413/155332018-10-03T01:02:34Z2017-01-01T00:00:00ZSome amenability properties on segal algebras.
It has been realized that the definition of amenability given by B. E. Johnson in
his Classical Memoir of American Mathematical Society in 1972 is too restrictive
and does not allow for the development of a rich general theory. For this reason,
by relaxing some of the constraints in the definition of amenability via restricting
the class of bimodules in question or by relaxing the structure of the derivations,
various notions of amenability have been introduced after the pioneering work
of Johnson on amenability in Banach algebras. This dissertation is focused on
six of these notions of amenability in Banach algebras, namely: contractibility,
amenability, weak amenability, generalized amenability, character amenability and
character contractibility. The first five of these notions are studied on arbitrary
Banach algebras and the last two are studied on some classes of Segal algebras.
In particular, results on hereditary properties and several characterizations of
these notions are reviewed and discussed. Indeed, we discussed the equivalent
of these notions with the existence of a bounded approximate diagonal, virtual
diagonal, splitting of exact sequences of Banach bimodules and the existence of a
certain Hahn-Banach extension property. Also, some relations that exist between
these notions of amenability are also established. We show that approximate contractibility
and approximate amenability are equivalent. Some conditions under
which the amenability of the underlying group of a Segal algebra implies the character
amenability of the Segal algebras are also given. Finally, some new results
are obtained which serves as our contribution to knowledge.
Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban 2017.
2017-01-01T00:00:00Z