At the Mathematics department office
Appointment on Visitation important
Topic: Fixed Points Of Multivalued Maps In Multiplicative Metric Spaces
The concept of multiplicative metric spaces was introduced in 2008 by Bashirov et al from the realization that the concepts of multiplicative derivatives (*derivative) and multiplicative integrals (*integral) are based on ordinary limit operation as alternative to the standard metric spaces.
Fixed points of single and multivalued maps of standard metric spaces and fixed points of single valued maps om multiplicative metric spaces have been widely delved into; however, few researchers have worked on fixed points of multivalued maps in multiplicative metric spaces.
The link between fixed point theorems on standard metric spaces and multiplicative metric spaces was attempted to be established by Dosenovic et al in 2016, however, it was limited to single valued maps.
My research proves fixed point theorems on multivalued maps in the setting of multiplicative metric spaces using a methodology that extends the method used by Dosenovic et al to multivalued maps. This research further proves fixed point theorems of multivalued mappings on graph endowed multiplicative metric spaces. Exploring further, on observing the striking similarity between contractive maps on spaces endowed with a graph and $alpha-psi$ contractions, attempt was made to extend the result of Ali et al in the settings of multiplicative metric spaces endowed with a graph.
|1.||Ph.D (Mathematics)||UNIVERSITY OF LAGOS, AKOKA, LAGOS||NaN|
FIXED POINTS OF SINGLEVALUED AND MULTIVALUED MAPS IN SPACES WITH ALTERATION OF THE TRIANGLE INEQUALITY
With abundant literature in metric spaces, rectangular metric spaces and multiplicative metric spaces, it is natural to investigate possible alterations of the triangle inequality for unification and generalization purposes.
Indeed, while the standard triangle inequality relates the distance between two points and the sum of their distances with another point, alterations of the triangle inequality vary from replacing the sum with multiplication to involving more points.
My current research is focused on the existence of fixed point of contractive maps on such spaces. The maps considered are contractive in some sense, with the use of comparison functions, partial order or by endowing the space with directed or undetected graphs.
The aim of the research work is to explore possible alterations of the triangle inequality in order to generalize existing fixed point results for single and multivalued maps on metric-type spaces. Furthermore, the research aims at investigating contractive conditions involving binary relations.
The research is literature based. A survey of relevant literatures was carried out. To obtain new results, known types of triangle inequality are being altered to accommodate operations other than sum and multiplication. The use of comparison functions, partial order or by endowing the space with directed or undetected graphs will be employed in the establishment of fixed points on metric-type spaces.
At the end of the research, generalized theorems on fixed points for single and multivalued maps on spaces with altered triangle inequality would have been established.
Contribution to Knowledge:
The results from the research will fill the vacuum between existing metric-type spaces with altered triangle inequality and proffer a generalized metric-type space which will be encompassing with relation to newly established axioms.
IGE AMINAT is a Lecturer II at the Department of Mathematics
IGE has a Ph.D in Mathematics from UNIVERSITY OF LAGOS, AKOKA, LAGOS