Uniform Treatment of Jensen’s Inequality by Montgomery Identity

We generalize Jensen’s integral inequality for real Stieltjes measure by using Montgomery identity under the effect of n − convex functions; also, we give different versions discrete along with its converses weights. As an application, generalized variants Hermite–Hadamard inequality. has a great importance as many inequalities can be obtained from in id="M2"> q calculus and fractional integrals. Also, applications information theory our results, especially Zipf Hybrid Zipf–Mandelbrot entropies.