Jensen type inequalities for twice dierentiable functions


Authors

Abdallah El Frissi - Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, Algeria. Benharrat Belaïdi - Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, Algeria. Zinelaâbidine Lareuch - Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (UMAB), B. P. 227 Mostaganem, Algeria.


Abstract

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.


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ISRP Style

Abdallah El Frissi, Benharrat Belaïdi, Zinelaâbidine Lareuch, Jensen type inequalities for twice dierentiable functions, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 5, 350--356

AMA Style

El Frissi Abdallah, Belaïdi Benharrat, Lareuch Zinelaâbidine, Jensen type inequalities for twice dierentiable functions. J. Nonlinear Sci. Appl. (2012); 5(5):350--356

Chicago/Turabian Style

El Frissi, Abdallah, Belaïdi, Benharrat, Lareuch, Zinelaâbidine. "Jensen type inequalities for twice dierentiable functions." Journal of Nonlinear Sciences and Applications, 5, no. 5 (2012): 350--356


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