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In this paper, we consider some new classes of log-preinvex functions. Several properties of the log-preinvex functions are studied. We also discuss their relations with convex functions. Several interesting results characterizing the log-convex functions are obtained. Optimality conditions of differentiable strongly log-preinvex are characterized by a class of variational-like inequalities. Results obtained in this paper can be viewed as significant improvement of previously known results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of harmonic preinvex functions, which are called harmonic h-preinvex functions. Several new Ostrowski-type inequal- ities for harmonic h-preinvex functions via Riemann-Liouville fractional integrals are established. Some special cases are also discussed, which appears to be new ones. The results obtained in this paper continue to hold for these cases. Interested readers are encouraged to find the applications of the harmonic h-preinvex functions in pure and applied sciences. This is an interesting topic for future research. [ABSTRACT FROM AUTHOR]