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

Chunyan Luo and Cuiling Wang ()
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Chunyan Luo: School of Mathematical Sciences, Xiamen University, Xiamen 361005, P. R. China
Cuiling Wang: School of Mathematical Sciences, Xiamen University, Xiamen 361005, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-26

Abstract: This paper investigates some properties of (σ,h)-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 (σ,h)-convex functions and elucidate various properties associated to them. Subsequently, we utilize generalized (σ,h)-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 h-convex functions, we introduce an alternative definition for generalized (σ,h)-convex functions and present concise yet rigorous proof of several main results. The results corroborate and extend certain conclusions drawn from proofs existing research.

Keywords: Generalized (σ; h)-Convex Function; Local Fractional Integral; Hermite–Hadamard-Type Inequality (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501421

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