Sahand Communications in Mathematical Analysis (Jun 2022)

On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals

  • Huseyin Budak,
  • Candan Can Bilişik,
  • Mehmet Sarikaya

DOI
https://doi.org/10.22130/scma.2022.539417.992
Journal volume & issue
Vol. 19, no. 2
pp. 65 – 79

Abstract

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In this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of $\phi (x)=\varpi \left( \frac{\kappa _{1}\kappa _{2}}{\mathcal{\varkappa }}\right) $ is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [34] under the condition $\phi ^{\prime }\left( \kappa_{1}+\kappa _{2}-\mathcal{\varkappa }\right) \geq \phi ^{\prime }(\mathcal{\varkappa })$ instead of harmonically convexity of $\varpi $. Moreover, some new inequalities for $k$-fractional integrals are given as special cases of main results.

Keywords