AUN professors have proposed a new class of mathematical function with huge potential applications for engineering, especially in the areas of space exploration, electrostatics, and fluid flow, as well as atomic and nuclear physics.
Making the proposal at a seminar on campus, Dr Moses Omuya and Dr Adewale James, both of SAS, observed that while the generalized Bessel function may have elicited interest from scholars, there is the need to determine the coefficient bounds functions belonging to a subclass of Bessel function so that it can find more specific applications. They, therefore, obtained a Fekete-Szego type of inequalities for the new class proposed.
Dr. Omuya explained that studies on the properties of analytic univalent function, commonly referred to as Geometric Function Theory (GFT), have been challenged by the coefficient problem. “Generally, most functions have large coefficients, but for this class of functions, however, their coefficients are not too large. We are interested in how the coefficient of these functions affects the geometric behavior of the function in the image domain,” he said.
Their study is on class of functions derived from the generalized Bessel function and is intended to determine the geometric properties, such as multivalence, convexity, and starlikeness of the class. The mathematicians arrived at their theorem with the use of various small axioms called lemmas. They were, however, only able to determine the bound subclass of the multivalent Bessel function, and are continuing more study on other geometric properties of this new subclass.
The respondent, Dr. Osho Ajayi, noted that this kind of investigation is one that does not really have immediate direct application, but that has huge potential that may not be visible in the next 50 years to address real-life problems. He commended the researchers for thinking ahead of their time. Dr James, who co-authored the paper, remarked that pure mathematics provides the needed tools in form of theorems that may appear abstract in nature but serve as the basis on which other fields of mathematics and engineering draw their applications and relevance.
Dr. Omuya, who holds a PhD in Complex Analysis, will present the paper titled “Coefficient Bounds for Certain Subclass of Multivalent Bessel Functions of Complex Order” at the 36th Nigerian Mathematical Society conference coming up in Makurdi, Benue State, from May 9-12. His research interests are in the areas of univalent function theory, special functions, fractional calculus, and applications.
By Omorogbe Omorogiuwa