The Ostrowski inequality for $ s $-convex functions in the third sense

Gültekin Tınaztepe; Sevda Sezer; Zeynep Eken; Sinem Sezer Evcan; Gültekin Tınaztepe; Sevda Sezer; Zeynep Eken; Sinem Sezer Evcan

doi:10.3934/math.2022310

AIMS Mathematics

2022, Volume 7, Issue 4: 5605-5615. doi: 10.3934/math.2022310

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Research article

The Ostrowski inequality for $ s $-convex functions in the third sense

1.
Vocational School of Technical Sciences, Akdeniz University, Antalya, Turkey
2.
Department of Mathematics and Science Education, Faculty of Education, Akdeniz University, Antalya, Turkey

Received: 21 October 2021 Revised: 28 December 2021 Accepted: 30 December 2021 Published: 10 January 2022
MSC : 26A51

In this paper, the Ostrowski inequality for $ s $-convex functions in the third sense is studied. By applying Hölder and power mean integral inequalities, the Ostrowski inequality is obtained for the functions, the absolute values of the powers of whose derivatives are $ s $-convex in the third sense. In addition, by means of these inequalities, an error estimate for a quadrature formula via Riemann sums and some relations involving means are given as applications.
- convexity,
- inequality,
- Ostrowski inequality,
- convex function,
- $ s $-convex function
Citation: Gültekin Tınaztepe, Sevda Sezer, Zeynep Eken, Sinem Sezer Evcan. The Ostrowski inequality for $ s $-convex functions in the third sense[J]. AIMS Mathematics, 2022, 7(4): 5605-5615. doi: 10.3934/math.2022310

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Abstract

In this paper, the Ostrowski inequality for $ s $-convex functions in the third sense is studied. By applying Hölder and power mean integral inequalities, the Ostrowski inequality is obtained for the functions, the absolute values of the powers of whose derivatives are $ s $-convex in the third sense. In addition, by means of these inequalities, an error estimate for a quadrature formula via Riemann sums and some relations involving means are given as applications.

References

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