On Jensen-McShane’s inequality

Jessen's functional, its properties and applications

“…Finally, let's mention that, according to Remark 3, all the results from this section are generalizations of appropriate results from paper [10].…”

“…Jessen's inequality was extensively studied during the eighties and early nineties of the last century (see papers [9], [11], [15], [18], [19], [20], [23]). Very recently,Čuljak et al (see [10]) generalized Jessen's relation (5). Namely, suppose Φ is continuous convex function on real interval, p, q ∈ L(E, R) are non-negative functions, and let the non-negative constants m and M exist such that…”

Superadditivity of the Levinson functional and applications

“…Here, we refer to its version in the above setting with a linear functional defined on a linear class of functions (see [11, p. 47], see also [3]). …”

Criteria Enlargement for an Inequality Between Quasi-Arithmetic Means

“…In the next two corollaries, the extensions of the multiplicative type inequality and the additive type inequality investigating in [9] and [4] are given.…”