Geodesic
Jensen type inequalities for twice dierentiable functions
El Frissi, Abdallah 1 ; Belaïdi, Benharrat1 ; Lareuch, Zinelaâbidine1
1 Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, Algeria
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 5, p. 350-356.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we give some Jensen-type inequalities for $\varphi: I\rightarrow\mathbb{R}, I=[\alpha,\beta ]\subset\mathbb{R}$ where $\varphi$ is a continuous function on $I$; twice differentiable on $I^°=(\alpha,\beta )$ and there exists $m = \inf _{x\in I^°} \varphi ''(x)$ or $M = \sup_{x\in I^°}\varphi '' (x)$. Furthermore, if $\varphi ''$ is bounded on $I^°$ ; then we give an estimate, from below and from above of Jensen inequalities.
DOI : 10.22436/jnsa.005.05.05
Classification : 26D15
Keywords: Jensen inequality, Convex functions, Twice differentiable functions

El Frissi, Abdallah  1 ; Belaïdi, Benharrat 1 ; Lareuch, Zinelaâbidine 1

1 Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, Algeria 
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El Frissi, Abdallah ; Belaïdi, Benharrat; Lareuch, Zinelaâbidine. Jensen type inequalities for twice dierentiable functions. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 5, p. 350-356. doi : 10.22436/jnsa.005.05.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.05.05/

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