The concept of convexity is one of the most important research area in many branches of mathematics, especially optimization, probability and statistics. Due to extensive applications of convex functions in different fields of pure and applied sciences, many researchers have paid much attention to study and investigate the theory of convex functions. In recent years, several generalizations and extensions have been considered for the concept of convexity. One of the most important generalizations of convex functions is that of preinvex functions. A number of studies have shown that the theory of convexity has a closely relationship with the theory of inequalities. The concept of inequality has an important place in literature, since it provides a broader setting to study different fields of pure and applied sciences. On the other hand, the concept of multiplicative calculus or non-Newtonian calculus has emerged as a new kind of derivative and integral by changing the roles of addition and subtraction with multiplication and division. In this study, new integral inequalities are established in the setting of multiplicative calculus for multiplicatively P-preinvex functions which are extensions of convex functions. The results obtained in this work can be viewed as generalization of the corresponding ones in the literature.
Anahtar Kelimeler: Preinvex function, Multiplicatively P-preinvex function, Integral inequalities, Multiplicative calculus