Hermite-Hadamard type inequalities for MT_{m}-preinvex functions

What is it about?

In the present paper, the notion of MT_{m}-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT_{m}-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MT_{m}-preinvex functions via classical integrals and Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given. These results not only extend the results appeared in the literature, but also provide new estimates on these types.

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Why is it important?

This new notion of MT_{m}-preinvex functions introduced can help all new scientist and researcher in the field of inequalities to find new generalizations of Hermite-Hadamard and Ostrowski type inequalities for other classes of preinvex functions and to obtain new estimates on these types.

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