ON MULTIPLICATIVE (s, P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS

In this paper, we propose a fresh conception about convexity, known as the multiplicative (s, P)-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 *differentiable (s, P)-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.