Results 101 to 110 of about 586 (111)

A counterpart to Jensen-Steffensen's inequality

Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, 2003
In this note a companion inequality to the Jensen-Steffensen inequality is ...
Pečarić, Josip, Elezović, Neven
openaire   +1 more source

Jensen-Steffensen Inequality: Accentuate the Negative

2023
Let f:I→R, where I is an interval in ℝ, be a convex function on I, and x=(x₁,⋯,x_{n})∈Iⁿ. If p=(p₁,⋯,p_{n}) is a nonnegative real n-tuple such that P_{n}=∑_{i=1}ⁿp_{i}>0 then the well-known Jensen inequality f((1/(P_{n}))∑_{i=1}ⁿp_{i}x_{i})≤(1/(P_{n}))∑_{i=1}ⁿp_{i}f(x_{i}) jen holds.
openaire  

On some general inequalities of the Jensen-Steffensen type

2008
We present a pair of general inequalities related to the Jensen-Steffensen inequality for convex functions. We show that the discrete Jensen-Steffensen inequality, as well as a discrete Slater type inequality, can be obtained from these general inequalities as their special cases. We also prove that one of our general companion inequalities, under some
Klaričić Bakula, Milica, Matić, Marko, Pečarić, Josip   +2 more
openaire   +1 more source

Conversions of the Jensen-Steffensen and Jensen-Mercer inequalities

2010
We establish conversions of the Jensen-Steffensen and Jensen-Mercer inequalities. We also use so caled exp-convex method to obtain some new inequalities related to those converse inequalities.
Klaričić Bakula, Milica, Ivelić Bradanović, Slavica, Pečarić, Josip   +2 more
openaire   +1 more source

Generalization of Jensen's and Jensen- Steffensen's inequalities and their converses by Hermite's polynomial and majorization theorem

Advances in Mathematics, 2015
In this paper, using majorization theorems and Hermite's interpolating polynomials we obtain results concerning Jensen's and Jensen- Steffensen's inequalities and their converses in both the integral and the discrete case. We give bounds for identities related to these inequalities by using \v{; ; ; C}; ; ; eby\v{; ; ; s}; ; ; ev functionals.
Pečarić, Josip, Vukelić, Ana, Aras-Gazić, Gorana   +2 more
openaire   +2 more sources

On the bounds for the normalized Jensen functional and Jensen-Steffensen inequality

2016
We consider the inequalities for normalized Jensen functional, recently introduced by S.S. Dragomir. We give an alternative proof of such inequalities and prove another similar result for the case when f is a convex function on an interval in the real line, while p and q satisfy the conditions for Jensen-Steffensen inequality.
Barić, Josipa, Pečarić, Josip
openaire  

Jensen-Steffensen inequality: old and new

2016
{;Let $I$ be an interval in $\mathbb{;R};$ and $f:I\rightarrow \mathbb{;R};$ a convex function on $I$.\ If $\boldsymbol{;\xi };=\left( \xi _{;1};, \cdots , \xi _{;m};\right) $ is any $m$-tuple in $I^{;m};$ and $\boldsymbol{;p};=\left( p_{;1};, \cdots , p_{;m};\right) $ any nonnegative $m$-tuple such that $% \sum_{;i=1};^{;m};p_{;i};>0$, then the well ...
openaire   +1 more source

Generalizations and refinements of the Jensen-Steffensen and its associated inequalities

2011
U disertaciji je razmatrana Jensen-Steffensenova i njoj srodne nejednakosti. Dan je niz profinjenja i poopćenja u različitim prostorima za razne klase funkcija nejednakosti Jensen-Steffensenova tipa te srodnih rezultata. Disertacija je podijeljena u šest poglavlja.
openaire  

New improvements of Jensen’s type inequalities via 4-convex functions with applications

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021
Muhammad Adil Khan, Shahid Khan, Josip E Pečarić   +2 more
exaly  

Jensen's and Jensen–Steffensen's Inequalities

1992
openaire   +1 more source