In this paper, we generalize and refine some Berezin number inequalities for Hilbert space operators. Namely, the Hermite-Hadamard inequality other recent results by using concept of superquadraticity convexity. Then extend these number. Among inequalities, it is shown that if S, T ? L(H(?)) such ber(T) ber(|S|) f a nonnegative superquadratic function, then (ber (T)) ber(f (|S|)) ?ber (f (||S| ...

In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. c ©2016 All rights reserved.

Abstract In this article, the notion of interval-valued preinvex functions involving Riemann–Liouville fractional integral is described. By applying this, some new refinements Hermite–Hadamard inequality for operator are presented. Some novel special cases presented results discussed as well. Also, examples to validate our results. The established outcomes article may open another direction dif...

A review of results on Hermite–Hadamard (H-H) type inequalities in quantum calculus, associated with a variety classes convexities, is presented. In the various convexities this includes classical convex functions, quasi-convex p-convex (p,s)-convex modified (p,h)-convex tgs-convex η-quasi-convex ϕ-convex (α,m)-convex ϕ-quasi-convex and coordinated functions. Quantum H-H via preinvex functions ...