AN IMPROVEMENT OF HÖLDER INTEGRAL INEQUALITY ON FRACTAL SETS AND SOME RELATED SIMPSON-LIKE INEQUALITIES
Chunyan Luo, Yuping Yu, Tingsong Du
Abstract
The purpose of this work is to investigate some inequalities for generalized [Formula: see text]-convexity on fractal sets [Formula: see text], which are associated with Simpson-like inequalities. To this end, an improved version of Hölder inequality and a Simpson-like identity on fractal sets are established, in view of which we give several estimation-type results involving Simpson-like inequalities for the first-order differentiable mappings. Moreover, we provide five examples to illustrate our results. As applications with respect to local fractional integrals, we derive two inequalities according to [Formula: see text]-type special means and generalized probability density functions.
Topics & Concepts
MathematicsInequalityDifferentiable functionConvexityType (biology)FractalPure mathematicsMathematical analysisApplied mathematicsBiologyEcologyFinancial economicsEconomicsMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsOptimization and Variational Analysis