An equivalent condition to the Jensen inequality for the generalized Sugeno integral.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given

The Effect of Web-Based Education on Learning in Medical Sciences Students: A Review Study

Introduction: Web-based education has come to attention in recent decades. However, there is no consensus on the effect of this method on students’ learning. The purpose of this review study was to assess the effect of web-based education on learning in medical sciences students. Methods: This Review study was carried out by searching the databases of SID, Iran MEDEX, Science Direct and PubMed, ERIC and Google Scholar. Articles from 2011 to 2016 were searched using the keywords web-based education, online learning, online education, medical students and nursing students. Finally, 14 articles that met the inclusion criteria were selected for review. Results: Of the 14 studies, five had been conducted in Europe, eight in Asia and one in America. They employed a variety of research designs. Students’ scores in teacher-made exams were used as the measure of learning in 11 studies. Two studies used students’ self-evaluation scores and one study employed students’ views about their own skill as the measure of learning. Of the 11 quantitative studies, only six reported the positive effect of web-based education on students’ learning, while the other five could not confirm such an effect. Two studies also reported students’ participation in the program at a favorable level. Four studies assessed students’ satisfaction with the web-based program and reported that the majority of students were satisfied with the program. Conclusion: Although a significant part of the studies reported the positive effect of web-based education on students’ learning, about half of the studies found no significant difference between students’ learning in web-based education and traditional education

An equivalent condition to the Jensen inequality for the generalized Sugeno integral

Abstract For the classical Jensen inequality of convex functions, i.e., H ( 1 μ ( D ) ∫ D f d μ ) ≤ 1 μ ( D ) ∫ D H ∘ f d μ , $$\begin{aligned} H \biggl(\frac{1}{\mu(D)} \int_{D}f\,d\mu \biggr)\leq\frac{1}{\mu (D)} \int_{D} H\circ f\,d\mu, \end{aligned}$$ an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given

An equivalent condition to the Jensen inequality for the generalized Sugeno integral.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given