Uniform treatment of Jensen's inequality by Montgomery identity (Q2038557)

Summary: We generalize Jensen's integral inequality for real Stieltjes measure by using Montgomery identity under the effect of \(\mathfrak{n}\)-convex functions; also, we give different versions of Jensen's discrete inequality along with its converses for real weights. As an application, we give generalized variants of Hermite-Hadamard inequality. Montgomery identity has a great importance as many inequalities can be obtained from Montgomery identity in \(q\)-calculus and fractional integrals. Also, we give applications in information theory for our obtained results, especially for Zipf and Hybrid Zipf-Mandelbrot entropies.