Thesis Chapters by mbongeni mzamwakhe
We show that a poset of formal balls of the Sorgenfrey quasi-metric space satisfies the certain p... more We show that a poset of formal balls of the Sorgenfrey quasi-metric space satisfies the certain properties of topological spaces of completeness such as Yoneda-completeness equipped with sequentially Yoneda-completeness both form a dcpo. We show that a poset has a unique property when considering the least upper bounds. In this case, we use the ascending sequences.\newline
Moreover, there is an elegant research question whether a partial metric topology is also a quasi-metric topology? By following the work of Matthews, we show the equivalence of the two classes using a weighted quasi-metric space. On the other hand, we introduce the construction from the work of Jimmie Lawson to the maximal point space about questioning whether is it continuous, bounded complete dcpo has been established. Furthermore, we study the maximal point space being a Polish space where Lawson questioned that is every Polish space a maximal point space of a bounded complete $\omega$-continuous poset. The results to the further research questions of Lawson's work have been constructed.
In this thesis, Monte Carlo methods are elaborated in terms of the
notion of the performance of g... more In this thesis, Monte Carlo methods are elaborated in terms of the
notion of the performance of games of chance and observing their out-
comes based on sampling random numbers and calculating the volume
of possible outcomes. The basic tool of generating random numbers is
the Monte Carlo simulation. The variance reduction techniques and their
applications to pricing options are also being reviewed for their crucial
role in ensuring the reduction of the error occurrence in variance. More-
over, the use of deterministic low-discrepancy sequences, also known as
quasi-Monte Carlo methods for the valuation of complex derivative se-
curities are being described. Monte Carlo simulation is a widely used
tool in finance for computing the prices of options as well as their price
sensitivities, which are known as Greeks. Furthermore, background about
stochastic differential equations (SDEs) is introduced and defined in terms
of stochastic calculus.
Papers by mbongeni mzamwakhe
We show that a poset of formal balls of the Sorgenfrey quasi-metric space satisfies the certain p... more We show that a poset of formal balls of the Sorgenfrey quasi-metric space satisfies the certain properties of topological spaces of completeness such as Yoneda-completeness equipped with sequentially Yoneda-completeness both form a dcpo. We show that a poset has a unique property when considering the least upper bounds. In this case, we use the ascending sequences.\newline Moreover, there is an elegant research question whether a partial metric topology is also a quasi-metric topology? By following the work of Matthews, we show the equivalence of the two classes using a weighted quasi-metric space. On the other hand, we introduce the construction from the work of Jimmie Lawson to the maximal point space about questioning whether is it continuous, bounded complete dcpo has been established. Furthermore, we study the maximal point space being a Polish space where Lawson questioned that is every Polish space a maximal point space of a bounded complete $\omega$-continuous poset. The results to the further research questions of Lawson's work have been constructed.
Journal of Mathematics, 2018
In this paper, we introduce the concept of a rectangular metric-like space, along with its topolo... more In this paper, we introduce the concept of a rectangular metric-like space, along with its topology, and we prove some fixed point theorems for different contraction types. We also introduce the concept of modified metric-like spaces and we prove some topological and convergence properties under the symmetric convergence. Some examples are given to illustrate the new introduced metric type spaces.
In this paper, the Banach contraction principle theorem is proved in rectangular metric-like spac... more In this paper, the Banach contraction principle theorem is proved in rectangular metric-like spaces and rectangular metric spaces. The extension of fixed point theorems in rectangular metric type spaces is generalized by various contraction mappings to obtain new fixed point results of rectangular metric spaces, which are extended to rectangular metric-like spaces.
In this paper, I develop the use of Ekeland variational principle in certain types of fixed point... more In this paper, I develop the use of Ekeland variational principle in certain types of fixed point theorems such as Subrahmanyam type-, Meir-Keeler type-, and Suzuki type-fixed point theorems. I generalize fixed point theorems in terms of Ekeland variational principle.
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Thesis Chapters by mbongeni mzamwakhe
Moreover, there is an elegant research question whether a partial metric topology is also a quasi-metric topology? By following the work of Matthews, we show the equivalence of the two classes using a weighted quasi-metric space. On the other hand, we introduce the construction from the work of Jimmie Lawson to the maximal point space about questioning whether is it continuous, bounded complete dcpo has been established. Furthermore, we study the maximal point space being a Polish space where Lawson questioned that is every Polish space a maximal point space of a bounded complete $\omega$-continuous poset. The results to the further research questions of Lawson's work have been constructed.
notion of the performance of games of chance and observing their out-
comes based on sampling random numbers and calculating the volume
of possible outcomes. The basic tool of generating random numbers is
the Monte Carlo simulation. The variance reduction techniques and their
applications to pricing options are also being reviewed for their crucial
role in ensuring the reduction of the error occurrence in variance. More-
over, the use of deterministic low-discrepancy sequences, also known as
quasi-Monte Carlo methods for the valuation of complex derivative se-
curities are being described. Monte Carlo simulation is a widely used
tool in finance for computing the prices of options as well as their price
sensitivities, which are known as Greeks. Furthermore, background about
stochastic differential equations (SDEs) is introduced and defined in terms
of stochastic calculus.
Papers by mbongeni mzamwakhe
Moreover, there is an elegant research question whether a partial metric topology is also a quasi-metric topology? By following the work of Matthews, we show the equivalence of the two classes using a weighted quasi-metric space. On the other hand, we introduce the construction from the work of Jimmie Lawson to the maximal point space about questioning whether is it continuous, bounded complete dcpo has been established. Furthermore, we study the maximal point space being a Polish space where Lawson questioned that is every Polish space a maximal point space of a bounded complete $\omega$-continuous poset. The results to the further research questions of Lawson's work have been constructed.
notion of the performance of games of chance and observing their out-
comes based on sampling random numbers and calculating the volume
of possible outcomes. The basic tool of generating random numbers is
the Monte Carlo simulation. The variance reduction techniques and their
applications to pricing options are also being reviewed for their crucial
role in ensuring the reduction of the error occurrence in variance. More-
over, the use of deterministic low-discrepancy sequences, also known as
quasi-Monte Carlo methods for the valuation of complex derivative se-
curities are being described. Monte Carlo simulation is a widely used
tool in finance for computing the prices of options as well as their price
sensitivities, which are known as Greeks. Furthermore, background about
stochastic differential equations (SDEs) is introduced and defined in terms
of stochastic calculus.