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Discrete Jensen-type inequality for a harmonically convex function was established by Dragomir in [S. S. Dragomir, RGMIA Monographs, Victoria University, (2015)]. In [I. A. Baloch, A. H. Mughal, Y. M. Chu, M. De la Sen, Accepted in Aims Mathematics], Baloch et al. presented a variant of discrete Jensen-type inequality for harmonically convex functions. Moreover, they established a Jensen-type inequality for harmonically h-convex functions, and then they proved the variant of Jensen-type inequality for harmonically h-convex functions. Our results generalize and improve some earlier results in the literature (for example see [S. S. Dragomir, RGMIA Monographs, Victoria University, (2015)] and [I. A. Baloch, A. H. Mughal, Y. M. Chu, M. De la Sen, Accepted in Aims Mathematics]) for the said class. Additionally, using them gives us more interesting results.

Improvement and generalization of some results related to the class of harmonically convex functions and applications