Estimates of bounds on the weighted Simpson type inequality and their applications

Chunyan Luo; Yuping Yu; Tingsong Du; Chunyan Luo; Yuping Yu; Tingsong Du

doi:10.3934/math.2020298

AIMS Mathematics

2020, Volume 5, Issue 5: 4644-4661. doi: 10.3934/math.2020298

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Research article

Estimates of bounds on the weighted Simpson type inequality and their applications

Department of Mathematics, College of Science, China Three Gorges University, 443002 Yichang, China

Received: 30 April 2020 Accepted: 19 May 2020 Published: 26 May 2020
MSC : 26D10, 26D15, 41A55

Based on the established integral identity, some bounds involving the weighted Simpson type inequality are obtained where the first derivative of considered mappings is (m, h)-preinvex, boundedness or Lipschitzian. As applications, certain generalized inequalities in connection with weighted Simpson type quadrature formula, continuous random variables and F-divergence measures are investigated, respectively.
- Simpson type inequality,
- (m, h)-preinvex mapping,
- F-divergence measures
Citation: Chunyan Luo, Yuping Yu, Tingsong Du. Estimates of bounds on the weighted Simpson type inequality and their applications[J]. AIMS Mathematics, 2020, 5(5): 4644-4661. doi: 10.3934/math.2020298

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Abstract

Based on the established integral identity, some bounds involving the weighted Simpson type inequality are obtained where the first derivative of considered mappings is (m, h)-preinvex, boundedness or Lipschitzian. As applications, certain generalized inequalities in connection with weighted Simpson type quadrature formula, continuous random variables and F-divergence measures are investigated, respectively.

References

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