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Different Variations of Hermite-Hadamard Inequality Arising from New Generalized (m, h)-harmonic Godunova-Levin Preinvex Mappings |
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PP: 23-33 |
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doi:10.18576/amisl/130202
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Author(s) |
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Najia Riaz,
Mujahid Abbas,
Waqar Afzal,
Joshua Kiddy K. Asamoah,
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Abstract |
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| The connection between generalized convexity and mathematical inequalities is deeply rooted in convex analysis and operator theory. To put the ideas of preinvexity and convexity even closer together, we might state that preinvex functions are extensions of convex functions. In this article, we give a new definition for generalized convexity, which essentially generalizes harmonic convex, Godunova-Levin, preinvex, and m-convex functions, and we named them (m,h)-harmonic Godunova and Levin preinvex functions. In light of this new definition, we developed various new refinements and bounds for Hermite-Hadamard inequality, its product and symmetric forms, along with several interesting remarks and corollaries that lead to their results with other convex mappings, specifically s-convex, tgs-convex, harmonic convex and a variety of others. In order to support the main results, a number of non-trivial examples are provided. |
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