Functional Analysis
Lecturer II
Mathematics
At the Mathematics department office
Appointment on Visitation important
Topic: Applications Of O-metric / O-series To Calculus, Optimization And Machine Learning
Description: The concept of O-metric is new. O-metric is a metric-type that unifies existing metric-types and its application to fixed point theory has been explored. Further research into O-metric-types and extension of O-metric fixed point results to multi-valued mappings are interesting to explore. Outstandingly, the construction of O-metric space lead to the generalisation of the famous triangle inequality and this generalisation exposed the strong potentials of the application of the results of O-metrics to more interesting phenomena beyond fixed point theory. The composition of the binary operation in the triangle inequality now generalised as polygon Inequalities is expressed with the use of binary trees portraying uniqueness of path by the means of pattern of integers and functions. The polygon O-inequality is discovered to give better optimal measures than the existing inequality in literature. This discovery and the resulting series opens up novel applications to better estimates optimization and the extension of same to networking, derivatives and improved algorithms in Machine learning. This interest is a green field promising unique solutions.
# | Certificate | School | Year |
---|---|---|---|
1. | Ph.D (Mathematics) | UNIVERSITY OF LAGOS, AKOKA, LAGOS | 2023 |
O-metric Spaces: A Unification of Metric-type Spaces
My current research is focused on Metrical fixed point theory, topology and associated geometries. The research establishes the construction of a new metric-type with its self-distance and triangle inequality axioms generalising those of the metric-types existing in literature. It is demonstrated that the newly constructed novel metric-type called O-metric, unifies several existing metric-types in literature and births previously unknown metric-types such as division metrics and downward O-metrics, both of which are highly recognisable in real-world scenarios. The potency of the generalisation lies in the introduction of a triangle inequality that accommodates several binary operations and a compatible self-distance. Three sets of conditions are used to distinguish whether or not the generalisation is trivial and fixed point results can be transposed from those in metric spaces. The study matches the properties of the O-metric topology with conditions on the binary operation supported by the triangle inequality. The research also formulates polygon O-inequalities as generalisations of the widely used triangle inequality, by means of pattern of integers, with surprising applications in Topology and Geometry. The formulation gives rise to the novel notion of O-series, a completely new infinite generalised series used to prove new fixed point results in the general framework of O-metric spaces and highly applicable in Calculus.
IGE AMINAT is a Lecturer II at the Department of Mathematics
IGE has a Ph.D in Mathematics from UNIVERSITY OF LAGOS, AKOKA, LAGOS