ON MULTIPLICATIVE (s,P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS
YU PENG, Tingsong Du
Abstract
In this paper, we propose a fresh conception about convexity, known as the multiplicative [Formula: see text]-convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the [Formula: see text]differentiable [Formula: see text]-convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and Newton-type inequalities. To further verify the validity of our primary outcomes, we give a few numerical examples. As applications, we proffer a number of inequalities of multiplicative type in special means as well.
Topics & Concepts
ConvexityMultiplicative functionMathematicsFractional calculusCalculus (dental)InequalityApplied mathematicsPure mathematicsMathematical analysisMedicineEconomicsFinancial economicsDentistryMathematical Inequalities and ApplicationsMathematical functions and polynomialsMatrix Theory and Algorithms