In this paper, a new definition of (m, h1, h2, s)-Harmonically convex function is introduced by combining m-convex, (h1, h2)-convex, s-convex, and harmonically convex function. Nowadays the approach of combining different convex functions is being used to extend the mathematical inequalities. In this paper, H-H inequality is considered to extend the fact that the combination of two or more convex functions combines their properties also. This innovative approach of combining convex functions leads to new applications in a variety of domains, including mathematics as well as other fields. These given inequalities can be considered as refinements and improvements to previously established results.