I prove that there is a recursive function T that does the following: Let X be transitive and rud closed, and let X ′ be the closure of X ∪{X} under rud functions. Given a Σ0 formula φ(x) and a code c for a rud function f , T (φ, c, ~x) is a Σω formula such that for any ~a ∈ X, X ′ |= φ[f(~a)] iff X |= T (φ, c, ~x)[~a]. I make this precise and show relativized versions of this. As an applicatio...

We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left-hand side and the right-hand side of these inequalities and present seve...

Unfortunately, the original version of this article [1] contained an error. The author’s names and affiliations have not been included correctly. The correct names and affiliations are: HI Jensen, TD Thomsen, JW Larsen and J Markvart * Corresponding author: Hanne Irene Jensen, [email protected] 1 Kolding Hospital, part of Lillebaelt Hospital, Kolding, Denmark 2 Institute of Regional He...

Abstract: We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded as an important extension of stability...

We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi's inequality. The obtained results are then applied for establishing new mean-va...

We introduce a novel family of distances, called the chord gap divergences, that generalizes the Jensen divergences (also called the Burbea-Rao distances), and study its properties. It follows a generalization of the celebrated statistical Bhattacharyya distance that is frequently met in applications. We report an iterative concave-convex procedure for computing centroids, and analyze the perfo...

Keywords: Hermite–Hadamard inequalities Jensen's inequality Xiao–Srivastava–Zhang–Pečarić–Svrtan–Jensen type inequalities Refinements and extensions Convex functions a b s t r a c t The main object of this paper is to give several refinements and extensions of the Hermite–Hadamard and Jensen inequalities in n variables. Relevant connections of the results presented here and the various inequali...

Abstract. In this paper we establish the stability of Jensen’s functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and T (2,K), where K is an arbitrary commutative field with characteristic different from two. We also prove that any group A can be embedded into some group G such that the Jensen functional equa...

Examining Firstand Second-Order Factor Structures for News Credibility Robert N. Yale, Jakob D. Jensen, Nick Carcioppolo, Ye Sun & Miao Liu To cite this article: Robert N. Yale, Jakob D. Jensen, Nick Carcioppolo, Ye Sun & Miao Liu (2015) Examining Firstand Second-Order Factor Structures for News Credibility, Communication Methods and Measures, 9:3, 152-169, DOI: 10.1080/19312458.2015.1061652 To...

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; Φ((C) ∫ fdμ) ≤ (C) ∫ Φ(f)dμ, where f is Choquet integrable, Φ : [0,∞) −→ [0,∞) is convex, Φ(α) ≤ α for all α ∈ [0,∞) and μf (α) ≤ μΦ(f)(α) for all α ∈ [0,∞). Furthermore, we give some examples assuring both satisfaction ...