ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS

İMDAT İŞCAN
2014 Mathematical sciences and applications e-notes  
In this paper, a new general identity for differentiable mappings via Riemann-Liouville fractional integrals has been defined. By using of this identity, author has obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolutely value at certain powers are s-convex in the second sense. 2 for all x ∈ [a, b] . Theorem 1.3. Let f : [a, b] → R be a four times continuously differentiable mapping on (a, b) and f (4) ∞ = sup
more » ... and f (4) ∞ = sup x∈(a,b) f (4) (x) < ∞. Then the following inequality
doi:10.36753/mathenot.207633 fatcat:hon4ufffmjbu7e6omvistxdwba