THE SIMPSON-TYPE INTEGRAL INEQUALITIES INVOLVING TWICE LOCAL FRACTIONAL DIFFERENTIABLE GENERALIZED (s,P)-CONVEXITY AND THEIR APPLICATIONS

Yunxiu Zhou () and Tingsong Du
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Yunxiu Zhou: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P. R. China
Tingsong Du: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang, Hubei 443002, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-32

Abstract: Applying the local fractional integrals, a generalized identity involving the local second-order differentiable mappings is first developed in this paper. A series of fractal integral inequalities pertaining to Simpson type, for the mappings whose local second-order derivatives are generalized (s,P)-convex in absolute value at some power, are then deduced by the discovered identity. Finally, from an application perspective, a range of fractal outcomes with regard to β-type special means, Simpson numerical integrations, midpoint numerical integrations and wave equations are presented, correspondingly.

Keywords: Generalized (s; P)-Convexity; Simpson-type Integral Inequality; Local Fractional Theory (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X2350038X

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