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