Abstract.

In this paper, we consider and investigate the relative harmonic preinvex functions, which unifies several new known classes of harmonic preinvex functions. We derive several new integral inequalities such as Hermite-Hadamard, Simpson’s, trapezoidal for the relative harmonic preinvex functions. Since the relative harmonic preinvex functions include, convex function, harmonic convex functions, preinvex functions, relative harmonic convex and relative preinvex functions as special cases, results obtained in this paper continue to hold for these problems. Several open problems have been suggested for further research in these areas.

Keywords:

harmonic convex functions, preinvex functions, harmonic preinvex functions, hconvex functions, midpoint inequality, trapezoidal inequality, Simpson’s inequality, HermiteHadamard type inequality.