科研之友
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摘要
First, we construct a reformative version of the power-mean integral inequality in the sense of fractal space. Second, we define what we named as the generalized (s,P)-convex mappings, and investigate some related properties. Moreover, in accordance with the derived midpoint-type integral identities on fractal space, we establish certain improvements of the midpoint-type integral inequalities for mappings whose first-order derivatives in absolute value belong to the generalized (s,P)-convex mappings. As applications in association with local fractional calculus, we acquire three inequalities considering nu-type arithmetic mean and beta-logarithmic mean, numerical integration, as well as probability density mappings, respectively.
