关于 Hermite-Hadamard 类型不等式通过分数积分来对 - 凸函数进行概括
Muhammad Sadaqat Talha1, Tasawar Abbas2, Zhixiong Li3,4
1Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan.
Heliyon
|December 13, 2024
概括
本研究引入了使用卡图甘波拉分数积分的lambda-convex函数的新积分身份和不等式. 这些发现扩展了现有的数学不等式,并为分数计算提供了新的结果.
科学领域:
- 数学分析的数学分析
- 分数微积分的计算.
- 不平等理论 不平等理论
背景情况:
- 不等式的研究是各种数学领域的基础.
- 分数计算为广义化经典微积分概念提供了工具.
- 兰巴达凸函数代表了一类具有独特属性的函数.
研究的目的:
- 为了建立涉及lambda-convex函数的新的整体身份.
- 用卡图甘波拉的分数积分来扩展赫米特-哈达马德类型的不等式.
- 为了获得经典不平等的新奇结果,如霍尔德的,詹森的,的,和权力平均不平等.
主要方法:
- 卡图冈波拉分数积分演算子的应用.
- 为lambda-convex函数量身定制的整体身份的开发.
- 在分数计算框架内利用lambda-convex函数的特性.
主要成果:
- 确定了lambda-convex函数的新Hermite-Hadamard类型的不等式.
- 通过使用卡图甘波拉的分数积分来得出几个新的积分身份.
- 对于lambda-convex函数,Holder,Jensen,Young和Power Mean不等式的扩展版本被呈现出来.
结论:
- 这项研究成功地扩展和统一了微积分计算领域中的几个不平等现象.
- 获得的结果为lambda-convex函数的行为提供了新的见解.
- 这项工作为进一步研究不等式和分数微积分的交叉点提供了基础.
相关概念视频
Convolution Properties II
173
The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
173
Chebyshev's Theorem to Interpret Standard Deviation
4.1K
Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
4.1K
Convolution Properties I
137
Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
137
Second Derivatives and Laplace Operator
1.2K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Consider a scalar function. The curl of its...
1.2K
Line, Surface, and Volume Integrals
2.3K
A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a prescribed path. If the prescribed path is closed, the integrals reduce to a closed-line integral. The closed-contour integral of the vector field is referred to in terms of the circulation of the vector field around the closed path. A vector with zero circulation around every closed path is called a conservative field, while one with non-zero...
2.3K
Routh-Hurwitz Criterion I
169
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
169


