The Hermite-Hadamard inequality for $ s $-Convex functions in the third sense

Sevda Sezer; Sevda Sezer

doi:10.3934/math.2021448

AIMS Mathematics

2021, Volume 6, Issue 7: 7719-7732. doi: 10.3934/math.2021448

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Research article

The Hermite-Hadamard inequality for $ s $-Convex functions in the third sense

Sevda Sezer ^,

Department of Mathematics and Science Education, Faculty of Education, Akdeniz University, Antalya, Turkey

Received: 19 February 2021 Accepted: 10 May 2021 Published: 13 May 2021
MSC : 26A51

In this paper, the Hermite-Hadamard inequality for $ s $-convex functions in the third sense is provided. In addition, some integral inequalities for them are presented. Also, the new functions based on the integral and double integral of $ s $-convex functions in the third sense are defined and under certain conditions, the third sense $ s $-convexity of these functions are shown and some inequality relations for these are expressed.
- Hermite-Hadamard inequality,
- convex set,
- convex function,
- $ s $-convex function in the third sense
Citation: Sevda Sezer. The Hermite-Hadamard inequality for $ s $-Convex functions in the third sense[J]. AIMS Mathematics, 2021, 6(7): 7719-7732. doi: 10.3934/math.2021448

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Abstract

In this paper, the Hermite-Hadamard inequality for $ s $-convex functions in the third sense is provided. In addition, some integral inequalities for them are presented. Also, the new functions based on the integral and double integral of $ s $-convex functions in the third sense are defined and under certain conditions, the third sense $ s $-convexity of these functions are shown and some inequality relations for these are expressed.

References

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