Hermite-Hadamard type fractional integral inequalities for MT(m,ϕ)-preinvex functions
DOI:
https://doi.org/10.24193/subbmath.2017.4.03Keywords:
Hermite-Hadamard type inequality, MT-convex function, H¨older’s inequality, power mean inequality, Riemann-Liouville fractional integral, m-invex, P -function.Abstract
In the present paper, a new class of MT(m,ϕ)-preinvex functions is in- troduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT(m,ϕ)-preinvex functions are given. More- over, some generalizations of Hermite-Hadamard type inequalities for MT(m,ϕ)- preinvex functions that are twice differentiable via Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given. These general inequalities give us some new estimates for Hermite-Hadamard type fractional integral inequalities.
Mathematics Subject Classification (2010): 26A51, 26A33, 26D07, 26D10, 26D15.
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