Relative strongly harmonic convex functions and their characterizations

In this paper, we introduce a new class of harmonic convex functions with respect to an arbitrary non-negative function, which is called the strongly general harmonic convex function. We discuss some characterizations of strongly general harmonic convex functions. Relationship with other classes of convex functions are also discussed. Some special cases are discussed as applications of the main results. The ideas and techniques of this paper may be starting point for further research.