Generalized Fejér–Hermite–Hadamard type via generalized (h−m)-convexity on fractal sets and applications

Ohud Almutairi and Adem Kiliçman

Chaos, Solitons & Fractals, 2021, vol. 147, issue C

Abstract: In this article, we define a new class of convexity called generalized (h−m)-convexity, which generalizes h-convexity and m-convexity on fractal set Rα(0<α≤1). Some properties of this new class are discussed. Using local fractional integrals and generalized (h−m)-convexity, we generalized Hermite–Hadamard (H–H) and Fejér–Hermite–Hadamard (Fejér–H–H) types inequalities. We also obtained a new result of the Fejér–H–H type for the function whose derivative in absolute value is the generalized (h−m)-convexity on fractal sets. As applications, we studied some new inequalities for random variables, numerical integrations and generalized to special means.

Keywords: Fractal set; Generalized (h−m)-convexity; Hermite–Hadamard inequality; Fejér–Hermite–Hadamard inequality; Local fractional integral (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921002927

DOI: 10.1016/j.chaos.2021.110938

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