Notions sur la quasi-convexité et inégalités Intégrales classiques et fractionnaires

Abstract

To sum up, In this work we have studied some notions on quasi-convexity and integral inequalities classic and fractional, we have dealt with Hermite-Hedamard’s classic and fractional. We have achieved the main objective which is the study of some classical integral inequalities and we have established some results on fractional calculus. In the first chapter we have presented some basic notions and important tools of convexity and quasi-convexity, which led us to deal with Classical case of Hermite- Hadamard’s inequalities via convexity and via quas-convexity . Then we have discussed in the second chapter the k-Riemann-Liouville Fractional Integral and some special cases when k = 1, this case is Hermite-Hadamard inequality. The last chapter shed light on Hermite-Hadamard type inequalities for quasi-convex functions via katugampola fractional integrals which generalizes the previous results of k-Riemann-Liouville Fractional Integral and Hermite-Hadamard fractional integral. 49