Browsing by Author "Jele, Thokozani Cyprian Martin."

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Bounds on the extremal eigenvalues of positive definite matrices.
(2018) Jele, Thokozani Cyprian Martin.; Singh, Virath Sewnath.; Singh, Pravin.
The minimum and maximum eigenvalues of a positive de nite matrix are crucial to determining the condition number of linear systems. These can be bounded below and above respectively using the Gershgorin circle theorem. Here we seek upper bounds for the minimum eigenvalue and lower bounds for the maximum eigenvalue. Intervals containing the extremal eigenvalues are obtained for the special case of Toeplitz matrices. The theory of quadratic forms is discussed in detail as it is fundamental in obtaining these bounds.
Fixed point theory in various generalized metric-type spaces.
(2022) Jele, Thokozani Cyprian Martin.; Singh, Virath Sewnath.; Singh, Pravin.
In the theory of fixed points, there are numerous articles dealing with generalization of the basic Banach contraction mapping principle. There has been two lines of approach. The first one is concerned with generalizations of the contractive conditions on the mapping space. The other line of investigation deals with various generalizations of the metric spaces and the results that can be obtained in these new frameworks, referred to as metric-type spaces. In this thesis, we elected for the latter approach by providing a more general framework for a b-metric space , G-metric space and S-metric space. In this thesis, we proved that these new metric-type spaces equipped with various contractions type mappings have unique fixed points and provide numerous examples of each metric-type spaced mentioned.