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Ovaj rad istražuje ključni pojam konveksnih funkcija u matematičkoj analizi i optimizaciji, s fokusom na Hermitovu-Hadamardovu nejednakost. Cilj rada je proučiti generalizacije Hermite-Hadamardove nejednakosti, procijeniti njihovu preciznost i promjene rezultata u kontekstu različitih vrsta konveksnosti. Također, želi se proširiti primjenjivost Hermitove-Hadamardove nejednakosti na različite klase konveksnih funkcija i istražiti kako različite vrste konveksnosti utječu na tu nejednakost., This paper explores the key notion of convex functions in mathematical analysis and optimization, with a focus on the Hermit-Hadamard inequality. The aim of the paper is to study the generalizations of the Hermit-Hadamard inequality, evaluate their precision and changes in results in the context of different types of convexity. Additionally, it aims to extend the applicability of the Hermit-Hadamard inequality to various classes of convex functions and investigate how different types of convexity influence this inequality.

The main aim of this paper is to introduce a new class of convex functions, which is called (p,r)-convex functions. We derive some new Hermite-Hadamard type integral inequalities via (p,r)-convex functions. Some special cases are also discussed. These results can be considered as significant improvement of the known results. The technique and ideas of this paper may motivate further research.

A generalization is given of the extension of Hadamard's inequality to r -convex functions. A corresponding generalization of the Fink–Mond–Pecaric inequalities for r -convex functions is established.