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In this paper, we establish various inequalities for some differentiablemappings that are linked with the illustrious Hermite-Hadamard integralinequality for mappings whose derivatives are $s$-$(\alpha,m)$-convex.Thegeneralised integral inequalities contribute some better estimates than somealready presented. The inequalities are then applied to numerical integrationand some special means.

Generalisations of Integral Inequalities of Hermite-Hadamard type through Convexity