Harmonically m-Convex Set-Valued Function

This research introduces the concept of harmonically m-convex set-valued functions, combining harmonically m-convex functions and set-valued mappings. We establish fundamental properties and derive a Hermite-Hadamard-type inequality for these functions, generalizing classical results in convex analysis. The study provides a theoretical foundation with potential applications in optimization, variational analysis, and mathematical economics, where set-valued mappings are essential. This work advances the understanding of harmonic convexity in the context of set-valued analysis, offering new insights for both theoretical and applied mathematics.