Discussion on the fractional Bullen estimation for twice-differentiable functions in the context of non-Newtonian calculus

Abstract

UDC 517.5; 517.9

We examine the Bullen estimations for functions twice differentiable within an $AG$-multiplicative calculus model, as characterized by the fractional Riemann–Liouville operators. First, an identity was established to serve for this purpose. By~using this identity, new inequalities are derived and expand the scope of previously established results (obtained with the help of Riemann–Liouville integrals), utilizing the multiplicative absolute value and presuming multiplicative $h$-convexity in the context that $h$ is a $B$-function. Furthermore, we obtain similar results for $AG$-multiplicatively $s$-convex functions and $AG$-multiplicatively $P$-functions.