Title of article :
On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals
Author/Authors :
Budak ، Huseyin Department of Mathematics - Faculty of Science and Arts - Duzce University , Bilişik ، Candan Can Department of Mathematics - Faculty of Science and Arts - Duzce University , Sarikaya ، Mehmet Zeki Department of Mathematics - Faculty of Science and Arts - Duzce University
Abstract :
In this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of ϕ(x) = ϖ ( κ1κ2/ κ ) is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [34] under the condition ϕ ′ (κ1 + κ2 − κ) ≥ ϕ ′ (κ) instead of harmonically convexity of ϖ. Moreover, some new inequalities for k-fractional integrals are given as special cases of main results.
Keywords :
Hermite , Hadamard inequality , convex function , Bounded function
Journal title :
Sahand Communications in Mathematical Analysis
Journal title :
Sahand Communications in Mathematical Analysis
