scholarly journals New weighted inequalities for higher order derivatives and applications

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4419-4433 ◽  
Author(s):  
Samet Erden ◽  
Mehmet Sarikaya ◽  
Huseyin Budak
Keyword(s):  
Type Inequality ◽  
Random Variables ◽  
Higher Order ◽  
Weighted Inequalities ◽  
Absolute Value ◽  
Ostrowski Type Inequality ◽  
New Inequalities ◽  
Differentiable Mappings

We establish a new Ostrowski type inequality for (n+1)-times differentiable mappings which are bounded. Then, some new inequalities of Hermite-Hadamard type are obtained for functions whose (n+1) th derivatives in absolute value are convex. Spacial cases of these inequalities reduce some well known inequalities. With the help of obtained inequalities, we give applications for the kth-moment of random variables.

scholarly journals A general Ostrowski type inequality for double integrals

2002 ◽  
Vol 33 (4) ◽  
pp. 319-334
Author(s):  
G. Hanna ◽  
S. S. Dragomir ◽  
P. Cerone
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Two Dimensions ◽  
One Dimensional ◽  
Ostrowski Type Inequality ◽  
And Function ◽  
Interior Points ◽  
Double Integrals ◽  
Differentiable Mappings

Some generalisations of an Ostrowski Type Inequality in two dimensions for $n-$time differentiable mappings are given. The result is an Integral Inequality with bounded $n-$time derivatives. This is employed to approximate double integrals using one dimensional integrals and function evaluations at the boundary and interior points.

scholarly journals AN OSTROWSKI TYPE INEQUALITY FOR TWICE DIFFERENTIABLE MAPPINGS AND APPLICATIONS

2016 ◽  
Vol 21 (4) ◽  
pp. 522-532 ◽  
Author(s):  
Samet Erden ◽  
Huseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Numerical Integration ◽  
Type Inequality ◽  
Special Means ◽  
Ostrowski Type Inequality ◽  
Second Derivatives ◽  
Differentiable Mappings

We establish an Ostrowski type inequality for mappings whose second derivatives are bounded, then some results of this inequality that are related to previous works are given. Finally, some applications of these inequalities in numerical integration and for special means are provided.

An Ostrowski type inequality for derivatives of q-th power of s-convex functions via fractional integrals

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Muhamet Emin Özdemir ◽  
Çetin Yildiz
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Ostrowski Type Inequality ◽  
Derivatives Of ◽  
New Inequalities

AbstractIn this paper, we establish several new inequalities for

scholarly journals Some Ostrowski’S Type Inequalities For Functions Whose Second Derivatives Are S-Convex In The Second Sense

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Erhan Set ◽  
Mehmet Zeki Sarikaya, ◽  
M. Emin Ozdemir
Keyword(s):  
Absolute Value ◽  
Second Derivatives ◽  
New Inequalities ◽  
Differentiable Mappings

AbstractSome new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are 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.

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

Weighted higher order exponential type inequalities in metric spaces and applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huiju Wang ◽  
Pengcheng Niu
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Sobolev Spaces ◽  
Exponential Type ◽  
Metric Spaces ◽  
Type Inequality ◽  
Higher Order ◽  
Geodesic Space ◽  
Stratified Lie Groups ◽  
Weighted Case

AbstractIn this paper, we establish weighted higher order exponential type inequalities in the geodesic space {({X,d,\mu})} by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined on stratified Lie groups. A higher order exponential type inequality in a connected homogeneous space is also given.

The central limit problem for trimmed sums

1987 ◽  
Vol 102 (2) ◽  
pp. 329-349 ◽  
Author(s):  
Philip S. Griffin ◽  
William E. Pruitt
Keyword(s):  
Distribution Function ◽  
Random Variables ◽  
Random Variable ◽  
Limit Problem ◽  
Absolute Value ◽  
Trimmed Sums ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Central Limit Problem ◽  
Trimmed Sum

Let X, X1, X2,… be a sequence of non-degenerate i.i.d. random variables with common distribution function F. For 1 ≤ j ≤ n, let mn(j) be the number of Xi satisfying either |Xi| > |Xj|, 1 ≤ i ≤ n, or |Xi| = |Xj|, 1 ≤ i ≤ j, and let (r)Xn = Xj if mn(j) = r. Thus (r)Xn is the rth largest random variable in absolute value from amongst X1, …, Xn with ties being broken according to the order in which the random variables occur. Set (r)Sn = (r+1)Xn + … + (n)Xn and write Sn for (0)Sn. We will refer to (r)Sn as a trimmed sum.

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