Generalizations of Ostrowski type inequalities via $ F $-convexity

Alper Ekinci; Erhan Set; Thabet Abdeljawad; Nabil Mlaiki; Alper Ekinci; Erhan Set; Thabet Abdeljawad; Nabil Mlaiki

doi:10.3934/math.2022396

AIMS Mathematics

2022, Volume 7, Issue 4: 7106-7116. doi: 10.3934/math.2022396

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Research article

Generalizations of Ostrowski type inequalities via $ F $-convexity

1.
Bandirma Vocational High School, Bandirma Onyedi Eylul University, Balikesir, Turkey
2.
Faculty of Science and Arts, Ordu University, Ordu, Turkey
3.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 17 August 2021 Revised: 22 January 2022 Accepted: 30 January 2022 Published: 09 February 2022
MSC : 26A33, 26A51, 26D15

The aim of this article is to give new generalizations of both the Ostrowski's inequality and some of its new variants with the help of the $ F $-convex function class, which is a generalization of the strongly convex functions. Young's inequality, which is well known in the literature, as well as Hölder's inequality, was used to obtain the new results. Also we obtain some results for convex and strongly convex functions by utilizing these inequalities.
- convex functions,
- $ F $-convex functions,
- strongly convex functions,
- Ostrowski's inequality,
- Young's inequality
Citation: Alper Ekinci, Erhan Set, Thabet Abdeljawad, Nabil Mlaiki. Generalizations of Ostrowski type inequalities via $ F $-convexity[J]. AIMS Mathematics, 2022, 7(4): 7106-7116. doi: 10.3934/math.2022396

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Abstract

The aim of this article is to give new generalizations of both the Ostrowski's inequality and some of its new variants with the help of the $ F $-convex function class, which is a generalization of the strongly convex functions. Young's inequality, which is well known in the literature, as well as Hölder's inequality, was used to obtain the new results. Also we obtain some results for convex and strongly convex functions by utilizing these inequalities.

References

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