Korean J. Math. Vol. 32 No. 2 (2024) pp.349-364
DOI: https://doi.org/10.11568/kjm.2024.32.2.349

Note on Newton-type inequalities involving tempered fractional integrals

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Published: Jun 30, 2024
Keywords:
Newton formula, fractional calculus, tempered fractional integrals
Mathematics Subject Classification:
26A51, 26D15, 34A08

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Fatih Hezenci
Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, Turkiye
https://orcid.org/0000-0003-1008-5856
Huseyin Budak
Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, Turkiye

Abstract

We propose a new method of investigation of an integral equality associated with tempered fractional integrals. In addition to this, several Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established identity. Moreover, we establish some Newton-type inequalities with the help of H\"{o}lder and power-mean inequality. Furthermore, several new results are presented by using special choices of obtained inequalities.


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