Some inequalities for the generalized k-g-fractional integrals of convex functions

Abstract

. Let g be a strictly increasing function on ( a , b ) , having a continuous derivative g (cid:2) on ( a , b ) . For the Lebesgue integrable function f : ( a , b ) → C , we de fi ne the k-g-left-sided fractional integral of f by and the where the kernel k is de fi ned either on ( 0 , ∞ ) or on [ 0 , ∞ ) with complex values and integrable on any fi nite subinterval. In this paper we establish some trapezoid and Ostrowski type inequalities for the k - g fractional integrals of convex functions. Applications for Hermite-Hadamard type inequalities for generalized g -means and examples for Riemann-Liouville and exponential fractional integrals are also given. ∈ 0 , 1 ) the function k is de fi ned on , and : , . If de on , and K