The AUN School of Arts and Sciences (SAS) has kicked off its Seminar Series for the Fall 2023 semester. The seminar commenced with a paper presentation by Dr. Sirajo Yahaya of the Department of Mathematics and Statistics titled "Bilateral Multivalued Contractions in Metric Space."
The presentation took place in the Faculty Lounge of the Arts and Sciences Building on September 19, 2023, and attracted a lot of AUN community members, including faculty, staff, and students.
In his work, the concepts of Jaggi, Dass-Gupta, and Caristi-Ciric-type bilateral multivalued contractions are introduced in the framework of metric spaces. New conditions for the existence of fixed points for such contractions are analyzed. A few consequences in single-valued mappings, which include the conclusion of the main result of Chen et al. on bilateral contractions, are obtained. In addition, nontrivial examples are provided to support the validity of the results obtained herein.
Dr. Sirajo used different theorems in algebra and quadratic equations to solve the set problems in space measurement.
The conclusion of the work broadened the scope of the fixed point theory of multivalued mappings by incorporating the bilateral approaches. To this end, Jaggi-type bilateral multivalued contraction, Dass-Gupta type bilateral multivalued contraction, and Ciric-Caristi-type multivalued contraction are initiated, and the corresponding fixed point theorems are proved, with examples illustrating the hypotheses of the main results.
The ideas in the work, being discussed in the setting of metric spaces, are entirely fundamental. Hence, they can be improved upon when presented in generalized metric spaces such as b-metric spaces, F-metric spaces, and some other pseudo-metric or quasi-metric spaces.
Dr. Sirajo Yahaya belongs to many professional affiliations, including the Mathematics Association of Nigeria (MAN), the Nigerian Mathematical Society (NMS), and the Nigerian Association of Mathematical Physics (NAMP).
His research interests are Functional Analysis, Fixed Point Theory, and Best Proximity Point Theory.
Reported by John Abah