On the parameterized fractal integral inequalities and related applications

Abstract

The utilization of local fractional calculus to investigate inequalities has become a widespread research method, which has enriched the theory of inequalities. The current study, inspired by this methodology and combined with the parameterized approach, explores a series of novel inequalities in the fractal spaces. Firstly, a fractal Bullen-type inequality with one parameter is presented. Secondly, the integral identity involving two parameters is established in the fractal domains. As an effect of this outcome, we derive a series of parameterized inequalities related to local fractional differentiable functions that are generalized (s,P)-convex and generalized (s,P)-concave at absolute values, respectively. Several special cases are discussed in depth as well. Certain applications concerning the special means, the quadrature formulas and the probability density functions are delivered in the end.