scholarly journals On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 727 ◽  
Author(s):  
Dongming Nie ◽  
Saima Rashid ◽  
Ahmet Ocak Akdemir ◽  
Dumitru Baleanu ◽  
Jia-Bao Liu
Keyword(s):  
Numerical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Random Variables ◽  
Higher Moments ◽  
Weighted Inequalities ◽  
Convex Mapping ◽  
Error Estimations ◽  
Moments Of Random Variables

In this article, we aim to establish several inequalities for differentiable exponentially convex and exponentially quasi-convex mapping, which are connected with the famous Hermite–Hadamard (HH) integral inequality. Moreover, we have provided applications of our findings to error estimations in numerical analysis and higher moments of random variables.

scholarly journals On Weighted Simpson’s 38 Rule

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1933
Author(s):  
Mohsen Rostamian Delavar ◽  
Artion Kashuri ◽  
Manuel De La De La Sen
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Type Inequality ◽  
Random Variables ◽  
Numerical Approximations ◽  
Weighted Version ◽  
Definite Integrals ◽  
Special Means ◽  
Error Estimations ◽  
Moments Of Random Variables

Numerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: Simpson’s 13 rule or Simpson’s quadrature formula and Simpson’s 38 rule or Simpson’s second formula. The aim of the present paper is to extend several inequalities that hold for Simpson’s 13 rule to Simpson’s 38 rule. More precisely, we prove a weighted version of Simpson’s second type inequality and some Simpson’s second type inequalities for Lipschitzian, bounded variations, convex functions and the functions that belong to Lq. Some applications of the second type Simpson’s inequalities relate to approximations of special means and Simpson’s 38 formula, and moments of random variables are made.

scholarly journals Some integral inequalities for approximately h—convex functions and their applications

2021 ◽  
Vol 40 (2) ◽  
pp. 481-504
Author(s):  
Artion Kashuri ◽  
Muhammad Raees ◽  
Matloob Anwar
Keyword(s):  
Convex Function ◽  
Integral Inequality ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Integral Type ◽  
Special Cases ◽  
Hölder’S Integral Inequality ◽  
Error Estimations

In this paper, by applying the new and improved form of Hölder’s integral inequality called Hölder—Íşcan integral inequality three inequalities of Hermite—Hadamard and Hadamard integral type for (h, d)—convex functions have been established. Various special cases including classes for instance, h—convex, s—convex function of Breckner and Godunova—Levin—Dragomir and strong versions of the aforementioned types of convex functions have been identified. Some applications to error estimations of presented results have been analyzed. At the end, a briefly conclusion is given.

scholarly journals Some Weighted Inequalities for Higher-Order Partial Derivatives in Two Dimensions and Its Applications

2020 ◽  
Vol 26 (3) ◽  
pp. 345-368
Author(s):  
Samet Erden ◽  
M. Zeki Sarikaya
Keyword(s):  
Numerical Analysis ◽  
Cubature Formula ◽  
Random Variables ◽  
Higher Order ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Weighted Inequalities ◽  
Lebesgue Spaces ◽  
Partial Derivatives

We establish some Ostrowski type inequalities involving higher-order partial derivatives for two-dimensional integrals on Lebesgue spaces (L_{∞}, L_{p} and L₁). Some applications in Numerical Analysis in connection with cubature formula are given. Finally,  with the help of obtained inequality, we establish applications for the kth moment of random variables.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

scholarly journals The space $D$ in several variables: random variables and higher moments

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Svante Janson
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Random Variables ◽  
Higher Moments ◽  
Multilinear Form ◽  
Standard Case ◽  
Random Functions ◽  
Several Variables ◽  
Random Elements ◽  
Point Evaluations

We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a description of the dual space, and we show that a bounded multilinear form always is measurable with respect to the $\sigma$-field generated by the point evaluations. These results are used to study random functions in the space. (I.e., random elements of the space.) In particular, we give results on existence of moments (in different senses) of such random functions, and we give an application to the Zolotarev distance between two such random functions.

On Some Integral Inequalities Related to Hardy's

1977 ◽  
Vol 20 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Christopher Olutunde Imoru
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Jensen's Inequality ◽  
Hardy's Inequality ◽  
Special Case

AbstractWe obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.

A Note on the Moments of Random Variables

2007 ◽  
Vol 22 (2) ◽  
Author(s):  
Surath Sen ◽  
Elart von Collani
Keyword(s):  
Random Variables ◽  
Moments Of Random Variables
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