Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus

Abstract

UDC 517.5

We define a new class of functions expressed as a convex combination of differential characterizations affected by the multiplicative derivative. Multiplicative derivative is defined in a domain, which excludes zero. Hence, in this case, the defined subclass does not involve replacing the ordinary derivative with a multiplicative derivative. However, we have used the motivation behind the purpose of this restrictive calculus given by the circumstances that we have a more versatile calculus of Newton and Euler. Estimates involving the initial coefficients of the functions, which have Maclaurin series and belong to the given function class are our main results. Some examples, along with the graphs, are used to establish the inclusion and the closure properties. Moreover, we obtain the logarithmic and inverse coefficients for the analyzed function class.