TY - JOUR
ID - 252483
TI - On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Budak, Huseyin
AU - Can Bilişik, Candan
AU - Sarikaya, Mehmet Zeki
AD - Department of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey.
Y1 - 2022
PY - 2022
VL - 19
IS - 2
SP - 65
EP - 79
KW - Hermite-Hadamard inequality
KW - convex function
KW - Bounded function
DO - 10.22130/scma.2022.539417.992
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_252483.html
L1 - https://scma.maragheh.ac.ir/article_252483_5c418ef6a00ed8e07a0b5e2b742f20c3.pdf
ER -