AN IMPROVEMENT OF HÖLDER INTEGRAL INEQUALITY ON FRACTAL SETS AND SOME RELATED SIMPSON-LIKE INEQUALITIES

Chunyan Luo (), Yuping Yu () and Tingsong Du
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Chunyan Luo: Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China
Yuping Yu: Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China
Tingsong Du: Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-20

Abstract: The purpose of this work is to investigate some inequalities for generalized s-convexity on fractal sets ℠α, which are associated with Simpson-like inequalities. To this end, an improved version of Hölder inequality and a Simpson-like identity on fractal sets are established, in view of which we give several estimation-type results involving Simpson-like inequalities for the first-order differentiable mappings. Moreover, we provide five examples to illustrate our results. As applications with respect to local fractional integrals, we derive two inequalities according to α-type special means and generalized probability density functions.

Keywords: Simpson-Like Inequality; Local Fractional Integrals; Generalized s-Convex Functions (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501267

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