### AIMS Mathematics

2022, Issue 4: 5605-5615. doi: 10.3934/math.2022310
Research article

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

• 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.

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

### Related Papers:

• 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.

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