scholarly journals Some (p,q)-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 683 ◽  
Author(s):  
Humaira Kalsoom ◽  
Muhammad Amer ◽  
Moin-ud-Din Junjua ◽  
Sabir Hussain ◽  
Gullnaz Shahzadi
Keyword(s):  
Convex Functions ◽  
Integral Type ◽  
Partial Derivatives ◽  
Functions Of Two Variables ◽  
Right Hand ◽  
The Absolute ◽  
The Right ◽  
Quasi Convexity

In this paper, we present the preliminaries of ( p , q ) -calculus for functions of two variables. Furthermore, we prove some new Hermite-Hadamard integral-type inequalities for convex functions on coordinates over [ a , b ] × [ c , d ] by using the ( p , q ) -calculus of the functions of two variables. Furthermore, we establish an identity for the right-hand side of the Hermite-Hadamard-type inequalities on coordinates that is proven by using the ( p , q ) -calculus of the functions of two variables. Finally, we use the new identity to prove some trapezoidal-type inequalities with the assumptions of convexity and quasi-convexity on coordinates of the absolute values of the partial derivatives defined in the ( p , q ) -calculus of the functions of two variables.

Approximations by multivariate perturbed neural network operators

2017 ◽  
Vol 15 (03) ◽  
pp. 413-432 ◽  
Author(s):  
George A. Anastassiou
Keyword(s):  
Neural Network ◽  
Rate Of Convergence ◽  
Activation Function ◽  
Jackson Type ◽  
Partial Derivatives ◽  
Right Hand ◽  
Hidden Layer ◽  
The Right ◽  
Derivatives Of

This article deals with the determination of the rate of convergence to the unit of each of three newly introduced here multivariate perturbed normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the involved multivariate function or its high-order partial derivatives and that appears in the right-hand side of the associated multivariate Jackson type inequalities. The multivariate activation function is very general, especially it can derive from any multivariate sigmoid or multivariate bell-shaped function. The right-hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of multivariate Stancu, Kantorovich and quadrature types. We give applications for the first partial derivatives of the involved function.

scholarly journals Synchronization Error of Drum Kit Playing with a Metronome at Different Tempi by Professional Drummers

2011 ◽  
Vol 28 (5) ◽  
pp. 491-503 ◽  
Author(s):  
Shinya Fujii ◽  
Masaya Hirashima ◽  
Kazutoshi Kudo ◽  
Tatsuyuki Ohtsuki ◽  
Yoshihiko Nakamura ◽  
...  
Keyword(s):  
Time Series ◽  
The Other ◽  
Synchronization Error ◽  
Left Hand ◽  
Snare Drum ◽  
Right Hand ◽  
The Absolute ◽  
The Right

the present study examined the synchronization error (SE) of drum kit playing by professional drummers with an auditory metronome, focusing on the effects of motor effectors and tempi. Fifteen professional drummers attempted to synchronize a basic drumming pattern with a metronome as precisely as possible at tempi of 60, 120, and 200 beats per minute (bpm). In the 60 and 120 bpm conditions, the right hand (high-hat cymbals) showed small mean SE (∼2 ms), whereas the left hand (snare drum) and right foot (bass drum) preceded the metronome by about 10 ms. In the 200 bpm condition, the right hand was delayed by about 10 ms relative to the metronome, whereas the left hand and right foot showed small SE (∼1 ms). The absolute values of SE were smaller than those reported in previous tapping studies. In addition, the time series of SE were significantly correlated across the motor effectors, suggesting that each limb synchronized in relation to the other limbs rather than independently with the metronome.

Über die Vierfingerfurche und ihre Übergangsformen, insbesondere bei Zwillingen

1954 ◽  
Vol 3 (1) ◽  
pp. 50-83 ◽  
Author(s):  
Irmgard Tillner
Keyword(s):  
Left Hand ◽  
Female Sex ◽  
Right Hand ◽  
Average Population ◽  
Transitional Forms ◽  
Male Sex ◽  
The Absolute ◽  
Hereditary Character ◽  
The Right

SUMMARYWe researched a total number of 3974 persons for the frequency of simian lines and all the material is based on 375 monozygotic, 360 dizygotic, 226 twins of different sex and 2045 single persons of two groups of the population. We classified the material collected into three degrees of impress of the simian line: a little form « 3 », a middle form « 2 » and the classical simian line, called form « 1 ». The form « 3 », which was more frequent to be seen than the form « 1 » and « 2 » seems to contain characteristics of « accidental » genesis without any relation to classical simian lines. That was to be found especially in the case that the little form was only on the surface of one hand. In contrast to that the form on both hands allows the deduction, that there must exist a relation to simian lines. The relations between the forms « 1 » and « 2 » are more evident than these of the little form « 3 ».The classical simian line seems to be more frequent on the left hand and with the male sex than on the right hand and with the female sex. This picture is a counterpart to the behaviour of thenar patterns.The result of the average population ist applicable to twins, too. Furthermore it was possible to show by arithmetic, that the concordant reactions of the monozygotics and the discordant reactions of the dizygotics are based on the hereditary character of simian lines and their transitional forms. There is a remarcable difference between monozygotic and dizygotic which is caused by the fact, that discordance of monozygotic is to be found in the case that one partner is one-sided affected with. Moreover the discordant forms become less frequent, if the degree of impress increases. The dizygotics are in the inverse ratio.The absolute concordance, too, that means the same degree of impress on the same hands of both partners, is more frequently to be found in the case of monozygotic than in the case of dizygotic.

On: “Maximum uncertainty of interval velocity estimates” by Z. Hajnal and I. T. Serada (GEOPHYSICS, 46, November 1981, 1543‐1547).

Geophysics ◽  
1985 ◽  
Vol 50 (11) ◽  
pp. 1790-1790
Author(s):  
I. Késmárky
Keyword(s):  
Statistical Analysis ◽  
Practical Result ◽  
Interval Velocity ◽  
Right Hand ◽  
The Absolute ◽  
The Right

In these remarks I draw attention to some practical aspects of the paper by Hajnal and Serada. Although conclusions drawn from equation (27) are clear and concise, the statistical analysis of equation (26) would lead to a more practical result. Taking the absolute values of all the terms on the right‐hand side of equation (26) may lead to a pessimistic overestimate of [Formula: see text].

Coefficient inequalities for univalent starlike functions

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Milutin Obradović ◽  
Saminathan Ponnusamy
Keyword(s):  
Unit Disk ◽  
Complex Number ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Right Hand ◽  
Coefficient Inequalities ◽  
The Right ◽  
Necessary And Sufficient

AbstractLet A be the class of analytic functions in the unit disk $$\mathbb{D}$$ with the normalization f(0) = f′(0) − 1 = 0. In this paper the authors discuss necessary and sufficient coefficient conditions for f ∈ A of the form $$\left( {\frac{z} {{f(z)}}} \right)^\mu = 1 + b_1 z + b_2 z^2 + \ldots$$ to be starlike in $$\mathbb{D}$$ and more generally, starlike of some order β, 0 ≤ β < 1. Here µ is a suitable complex number so that the right hand side expression is analytic in $$\mathbb{D}$$ and the power is chosen to be the principal power. A similar problem for the class of convex functions of order β is open.

scholarly journals New Hermite-Hadamard type inequalities for m and (α, m)-convex functions on the coordinates via generalized fractional integrals

2021 ◽  
Vol 40 (6) ◽  
pp. 1449-1472
Author(s):  
Seth Kermausuor
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Second Order ◽  
Fractional Integrals ◽  
Absolute Value ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Functions Of Two Variables ◽  
Derivatives Of ◽  
Two Independent Variables

In this paper, we obtained a new Hermite-Hadamard type inequality for functions of two independent variables that are m-convex on the coordinates via some generalized Katugampola type fractional integrals. We also established a new identity involving the second order mixed partial derivatives of functions of two independent variables via the generalized Katugampola fractional integrals. Using the identity, we established some new Hermite-Hadamard type inequalities for functions whose second order mixed partial derivatives in absolute value at some powers are (α, m)-convex on the coordinates. Our results are extensions of some earlier results in the literature for functions of two variables.

scholarly journals On Hermite-Hadamard Type Inequalities fors-Convex Functions on the Coordinates via Riemann-Liouville Fractional Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Feixiang Chen
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Right Hand ◽  
The Right

We obtain some Hermite-Hadamard type inequalities fors-convex functions on the coordinates via Riemann-Liouville integrals. Some integral inequalities with the right-hand side of the fractional Hermite-Hadamard type inequality are also established.

scholarly journals HERMITE–HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHEN A POWER OF THE ABSOLUTE VALUE OF THE FIRST DERIVATIVE IS P-CONVEX

2011 ◽  
Vol 86 (1) ◽  
pp. 126-134 ◽  
Author(s):  
A. BARANI ◽  
S. BARANI
Keyword(s):  
Type Inequality ◽  
Absolute Value ◽  
Trapezoidal Formula ◽  
First Derivative ◽  
Right Hand ◽  
Special Means ◽  
The Absolute ◽  
The Right

AbstractIn this paper we extend some estimates of the right-hand side of a Hermite–Hadamard type inequality for functions whose derivatives’ absolute values are P-convex. Applications to the trapezoidal formula and special means are introduced.

Refinement of fejér inequality for convex and co-ordinated convex functions

2020 ◽  
Vol 70 (3) ◽  
pp. 585-598
Author(s):  
Kai-Chen Hsu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Beta Function ◽  
Right Hand ◽  
Fejér Inequality ◽  
The Right

AbstractIn this paper, we shall establish the co-ordinated convex function. It can connect to the right-hand side of Fejér inequality in two variables and thus a new refinement can be found. In addition, some applications to estimates for Euler’s Beta function are also given in the end.

scholarly journals Some Hermite-Hadamard Type Inequalities for Harmonicallys-Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Feixiang Chen ◽  
Shanhe Wu
Keyword(s):  
Convex Functions ◽  
Right Hand ◽  
The Right

We establish some estimates of the right-hand side of Hermite-Hadamard type inequalities for functions whose derivatives absolute values are harmonicallys-convex. Several Hermite-Hadamard type inequalities for products of two harmonicallys-convex functions are also considered.

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