Jensen-Steffensen's and related inequalities for superquadratic functions

Abramovich, Shoshana; Banić, Senka; Matić, Marko; Pečarić, Josip

doi:10.7153/mia-11-02

Cited by 6 publications

(5 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we quote some definitions and theorems that we use in this paper. More examples and properties of superquadratic functions can be found in [1,7,9] and its references.…”

Section: On Superquadratic Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Time Scales Integral Inequalities for Superquadratic Functions

Barić¹,

Bibi²,

Böhner³

et al. 2013

Journal of the Korean Mathematical Society

View full text Add to dashboard Cite

show abstract

“…Here we quote some definitions and theorems that we use in this paper. More examples and properties of superquadratic functions can be found in [1,7,9] and its references.…”

Section: On Superquadratic Functionsmentioning

confidence: 99%

“…Let ϕ : [0, ∞) → R be a superquadratic function and let x 0 ∈ [0, ∞). According to (1), there is a constant C(x 0 ) such that…”

Section: Jensen's Inequalitymentioning

confidence: 99%

Time Scales Integral Inequalities for Superquadratic Functions

Barić¹,

Bibi²,

Böhner³

et al. 2013

Journal of the Korean Mathematical Society

View full text Add to dashboard Cite

show abstract

“…This result yielded many generalizations and applications; see e.g. Abramovich et al (2005Abramovich et al ( , 2006Abramovich et al ( , 2008, Klaričić Bakula et al (2006, Barić et al (2010), Cheung et al (2006), Gavrea (2004), Matković et al (2006Matković et al ( , 2007Matković et al ( , 2008) and many others. Niezgoda (2009) has studied the following generalization of ( 22):…”

Section: Readsmentioning

confidence: 85%

Fujiwara’s inequality for synchronous functions and its consequences

Otachel

2023

Biometrical Letters

View full text Add to dashboard Cite

Summary The theory of inequalities is an essential tool in all fields of the theoretical and practical sciences, especially in statistics and biometrics. Fujiwara’s inequality provides relationships between expected values of products of random variables. Special cases of this inequality include important classical inequalities such as the Cauchy–Schwarz and Chebyshev inequalities. The purpose of this article is to prove Fujiwara’s inequality in abstract probability spaces with more general assumptions for random variables than those associated with monotonicity as found in the literature. This newly introduced property of random variables will be called synchronicity. As a consequence, we obtain inequalities originated by Chebyshev, Hardy–Littlewood–Pólya and Jensen–Mercer under new conditions. The results are illustrated by some examples constructed for specific probability measures and specific random variables. In biometrics, the obtained inequalities can be used wherever there is a need to compare the characteristics of experimental data based on means or moments, and the data can be modeled using functions that are synchronous or convex.

show abstract

“…First we quote from [2] Definition 1, Theorem A and Lemmas A and B basics of the set of superquadratic functions. Then we quote in Theorems B-E theorems proved in [3] and [4] on superquadratic functions which we either use or sharpen in the sequel (more on superquadratic functions see for instance [1,4,11] and its references); then we quote two theorems on convex (and Wright-convex) functions proved in [12] and [14] which we also refine. …”

Section: Introductionmentioning

confidence: 98%