REFINING RECURSIVELY THE HERMITE–HADAMARD INEQUALITY ON A SIMPLEX

2015 ◽  
Vol 92 (1) ◽  
pp. 57-67 ◽  
Author(s):  
MUSTAPHA RAÏSSOULI ◽  
SEVER S. DRAGOMIR
Keyword(s):  
Convex Function ◽  
Upper Bounds ◽  
Mean Value ◽  
Lower And Upper Bounds ◽  
Hadamard Inequality

In the present paper, a coupled algorithm refining recursively the Hermite–Hadamard inequality on a simplex is investigated. Our approach allows us to express the integral mean value $M_{f}$ of a convex function $f$ on a simplex as both the limit of sequences and sum of series involving iterative lower and upper bounds of $M_{f}$. Two examples of interest are discussed.

scholarly journals A note on the refinement of Hermite-Hadamard inequality

2021 ◽  
Vol 2106 (1) ◽  
pp. 012006
Author(s):  
Mochammad Idris
Keyword(s):  
Convex Function ◽  
Maximum Error ◽  
Mean Value ◽  
Hadamard Inequality ◽  
The Mean ◽  
Dyadic Decomposition

Abstract In this paper, we give the sharper bounds for the mean value of a convex function using dyadic decomposition. Our result is related with classical Hermite-Hadamard inequality. Moreover, using the result, we can determine the maximum error before calculating the numerical (trapezoidal) integral of the convex function.

scholarly journals KETAKSAMAAN HERMITE-HADAMARD TERHADAP INTEGRAL RIEMANN-STIELTJES

2012 ◽  
Vol 4 (1) ◽  
pp. 59
Author(s):  
Denny Ivanal Hakim ◽  
Hendra Gunawan
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Closed Interval ◽  
Mean Value ◽  
Stieltjes Integral ◽  
Power Mean ◽  
Real Numbers ◽  
Positive Real ◽  
Hadamard Inequality

The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. The Hermite-Hadamard inequality can be generalized by using the Riemann-Stieltjes integral mean value.  An application of the Hermite-Hadamard inequality with respect to Riemann-Stieltjes integral  for estimating the power mean of   positive real numbers by the aritmethic mean is given at the end of discussion.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

The Lower and Upper Bounds of Turán Number for Odd Wheels

2021 ◽  
Vol 37 (3) ◽  
pp. 919-932
Author(s):  
Byeong Moon Kim ◽  
Byung Chul Song ◽  
Woonjae Hwang
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Turán Number

scholarly journals Lower and upper bounds of quantum battery power in multiple central spin systems

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Li Peng ◽  
Wen-Bin He ◽  
Stefano Chesi ◽  
Hai-Qing Lin ◽  
Xi-Wen Guan
Keyword(s):  
Upper Bounds ◽  
Spin Systems ◽  
Lower And Upper Bounds ◽  
Battery Power
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