On interval-valued $\mathbb{K}$-Riemann integral and Hermite-Hadamard type inequalities

Zehao Sha; Guoju Ye; Dafang Zhao; Wei Liu; Zehao Sha; Guoju Ye; Dafang Zhao; Wei Liu

doi:10.3934/math.2021079

AIMS Mathematics

2021, Volume 6, Issue 2: 1276-1295. doi: 10.3934/math.2021079

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Research article

On interval-valued $\mathbb{K}$-Riemann integral and Hermite-Hadamard type inequalities

1.
College of Science, Hohai University, Nanjing, Jiangsu 210098, China
2.
School of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, China

Received: 25 July 2020 Accepted: 11 November 2020 Published: 16 November 2020
MSC : 26A51, 26D15, 26E25

We introduce the concepts of $\mathbb{K}$-Riemann integral and radial $\mathbb{K}$-g$H$-derivative for interval-valued functions. We also give some important properties of interval-valued $\mathbb{K}$-Riemann integral, and extend interval-valued Hermite-Hadamard type inequalities in the case of $\mathbb{K}$-Riemann integral. Several examples are shown to illustrate the results.
- interval-valued functions,
- radial $\mathbb{K}$-g$H$-derivative,
- $\mathbb{K}$-Riemann integral,
- Hermite-Hadamard type inequalities
Citation: Zehao Sha, Guoju Ye, Dafang Zhao, Wei Liu. On interval-valued $\mathbb{K}$-Riemann integral and Hermite-Hadamard type inequalities[J]. AIMS Mathematics, 2021, 6(2): 1276-1295. doi: 10.3934/math.2021079

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Abstract

We introduce the concepts of $\mathbb{K}$-Riemann integral and radial $\mathbb{K}$-g$H$-derivative for interval-valued functions. We also give some important properties of interval-valued $\mathbb{K}$-Riemann integral, and extend interval-valued Hermite-Hadamard type inequalities in the case of $\mathbb{K}$-Riemann integral. Several examples are shown to illustrate the results.

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