On Hermite-Hadamard type integral inequalities for preinvex and log-preinvex functions

Convexity and the generalization of convexity are one of the most important aspects in mathematical programming, optimization theory, equilibrum problems and variational problems. Hermite-Hadamard type inequality has become an important cornerstone in mathematical analysis and optimization and many other inequalities for convexity, invexity and preinvexity. Recently, it has been establihed some results of the right hand side of a Hermite-Hadamard type inequality. In this thesis, Some results of the left hand side of a Hermite- Hadamard type inequality were obtained for nonconvex functions whose derivatives absolute values are preinvex and log-preinvex, and those ressults were extened to several variables functions. Keywords : Convexity, invexity, Hermite-Hadamard inequality, preinvex functions, logpreinvex functions