Generalized Riemann-Liouville Fractional Integral Inequalities And Quantum Integral Inequalities

Based on the generalized Riemann-Liouville fractional integrals and quantum integrals,we study Hadamard-type fractional integral inequalities and quantum integral inequalities for several kinds of generalized convex functions.Taking different values for the parameters,we can obtain different types of integral inequalities.Some inequalities established in the paper are the generalizations of existing results in the literature.Chapter 1,we introduce the concepts of Riemann-Liouville fractional integrals and quantum integrals and expound the development of Hadamard-type inequality.Chapter 2,based on k-fractional integrals,we study the Hadamard-type inequalities of the generalized(m,h)-preinvex functions.Firstly we construct a new k-fractional integral identity.Then based on the identity,we establish some new k-fractional integral inequalities.Taking different values for the parameters,we can obtain different types of integral inequalities.Chapter 3,firstly we introduce the concept of?_m-path.Then we construct a k-fractional integral identity with multiple parameters,and establish some fractional integral inequalities for generalized(s,m)-preinvex functions.Finally,using the generalized(s,m)-preinvexity,we also obtain some integral inequalities of product type.Chapter 4,firstly we construct a Hadamard-Simpson-type quantum integral identity with multiple parameters.Then based on the new integral identity,we establish some quantum integral inequalities for(?,m)-convex functions.Meanwhile,using the(?,m)-convexity,we also obtain some integral inequalities of product type.Chapter 5,firstly we present a(p,q)-type quantum integral identity.Then based on the integral identity,we establish some(p,q)-type quantum integral inequalities for convex functions.Meanwhile,we establish some(p,q)-type quantum integral inequalities involving the products of two convex functions.Finally,based on the new integral identity,using the boundedness of a function and the Lipschitz condition,we also obtain some corresponding(p,q)-type quantum integral inequalities.Chapter 6,we summarize the main contents of this paper and provide some contents that need to be studied.