Amazing Jensen's Inequality | Ashish Khare Sir

2022/12/20 に公開
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Amazing Jensen's Inequality | Ashish Khare Sir

Jensen inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation; it is a simple corollary that the opposite is true of concave transformations.
Jensen's inequality generalizes the statement that the secant line of a convex function lies above the graph of the function, which is Jensen's inequality for two points: the secant line consists of weighted means of the convex function.
Named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906 building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889.
Jensen's inequality in ethe context of IIT JEE is very useful in
• Inequalities like AM greater than equal to GM, AM greater than equal to HM
• Theorems like mth power theorem
• Functional inequality
• Inequalities in an triangle
In this lecture series you will learn the complete details about Jensen Inequality from Ashish Khare Sir for IIT JEE. It is one of the most important topics of the IIT JEE Maths question paper - in IIT JEE Advanced and JEE Mains as well.
• Get the best IIT notes curated by experts.
• Solve important JEE Main and JEE Advanced 2023 questions
• Find IIT JEE Maths preparation tips and tricks.
• Crack IIT JEE 2023 Maths with these valuable IIT JEE preparation tips and tricks.
Jensen Inequality | Class 11 Maths | | JEE Mains 2023 | JEE Main 2023 | JEE Advanced 2023 | JEE Mains 2024 | JEE Main 2024 | JEE Advanced 2024 |

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