A NEW DEFINITION AND PROPERTIES OF QUANTUM INTEGRAL WHICH CALLS $\overline{q}$-INTEGRAL

Abstract

In this paper, we present a new definition of $q$-integral by using trapezoid pieces and we name second sense $q$-integral which is showed $ \overline{q}$-integral and we give some results and properties of $\overline{ q}$-integral. Finaly, we establish some new $\overline{q}$-Hermite-Hadamard type inequalities for convex functions.