Our aim in this article is to incorporate the notion of "strongly s-convex function" and prove a new integral identity. Some new inequalities of Simpson type for strongly s-convex function utilizing integral identity and Holder's inequality are considered.

We obtain a 3-fold Selberg integral formula. As a consequence we are able to compute the explicit value of the sharp constant in a trilinear fractional integral inequality due to Beckner.

The theory and applications of dynamic derivatives on time scales have recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-α derivatives which are a linear combination of delta and nabla dynamic derivatives on time scales. We prove a generalized version of Jensen’s inequality on time scales via the diamond-α integral and present som...

Abstract We give necessary and sufficient conditions for the Chebyshev integral inequality to be an equality.

Trapezoid inequality estimates the difference of integral mean a function on finite interval [a, b] and arithmetic its values at endpoints b. Quantum calculus is based diference principle or without concept limits. Euler-Jackson q-difference operator q-integral are discretization ordinary derivatives integrals they can be generalized to shifted versions arbitrary domain b]. In this paper we dis...

A more complete Young’s integral inequality on arbitrary time scales (unbounded above) is presented.