EXPLORATION OF (σ,h)-CONVEX FUNCTIONS ON FRACTAL SETS AND THEIR APPLICATIONS

This paper investigates some properties of [Formula: see text]-convex functions defined on fractal sets and discusses certain applications of such functions associated with or related to classical inequalities. To this end, we initially give the definition for generalized [Formula: see text]-convex functions and elucidate various properties associated to them. Subsequently, we utilize generalized [Formula: see text]-convex functions to obtain a variety of inequalities such as Jensen-type inequality, Hermite–Hadamard-type inequality, Karamata-type inequality and Ostrowski-type inequality. Finally, leveraging the concept of generalized [Formula: see text]-convex functions, we introduce an alternative definition for generalized [Formula: see text]-convex functions and present concise yet rigorous proof of several main results. The results corroborate and extend certain conclusions drawn from proofs existing research.