Reserarch On Two Kinds Of Integral Inequalities Based On Generalized Convex Functions

In this paper,some Hermite-Hadamard-type and Fejer-type integral inequalities of integer order are generalized into fractional integral inequalities.Using the generalized convexity and some classical inequalities,some new fractional integral inequalities are established.In chapter 1,we mainly introduce the Riemann-Liouville fractional calculus and the local fractional calculus and also review the development of Hermite-Hadamard and Fejer inequalities.In chapter 2,a new general identity for differentiable mappings via k-Riemann-Liouville intergrals is derived.Using(h,m)-convexity and the obtained equation,some new Hermite-Hadamard type integral inequalities are established.The results presented provide extensions of those given in earlier works.At the beginning of chapter 3,we restate the definition of invex set and preinvex functions.Then,some new trapezium-like k-Riemann-Liouville fractional inequalities with multiple parameters are established.Finally,the established trapezoidal inequalities are applied to the error estimation of cumulative distribution functions.In chapter 4,we introduce the generalized m-convex functions on the real linear fractal set Rα(0<α≤1)and study some properties for such mappings.In addition,we also establish a local fractional Hermite-Hadamard inequality of generalized m-convex functions.In chapter 5,we prove the Hermite-Hadamard-Fejer inequalitiy for generalized h-convex functions.Then,we establish a general identity via local fractional integrals.Using the generalized h-convexity and the obtained equation,some new Fejer-type integral inequalities are establishedIn chapter 6,we summarize the work of this paper,and look forward to the direction of the next research work.