Hermite-Hadamard type fractional integral inequalities for generalized beta (r, g)-preinvex functions.
Keywords:
Hermite-Hadamard type inequality, Hölder’s inequality, Minkowski’s inequality, Cauchy’s inequality, Power mean inequality, Riemann-Liouville fractional integral, s-convex function in the second sense, m-invex, P-functionAbstract
In the present paper, a new class of generalized beta (r, g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized beta (r, g)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized beta (r, g)-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see [1]), [2]), but also provide new estimates on these types.
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