scholarly journals Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas

2022 ◽  
Vol 6 (1) ◽  
pp. 33
Author(s):  
Sabah Iftikhar ◽  
Samet Erden ◽  
Muhammad Aamir Ali ◽  
Jamel Baili ◽  
Hijaz Ahmad
Keyword(s):  
Convex Functions ◽  
Cubature Formula ◽  
Applied Mathematics ◽  
Second Order ◽  
Absolute Value ◽  
Partial Derivatives ◽  
Cubature Formulas ◽  
Inequality Theory ◽  
Type Integral ◽  
Derivatives Of

Inequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied mathematics. We deal with Simpson’s second-type inequalities based on coordinated convex functions in this work. In this paper, we first introduce Simpson’s second-type integral inequalities for two-variable functions whose second-order partial derivatives in modulus are convex on the coordinates. In addition, similar results are acquired by considering that powers of the absolute value of second-order partial derivatives of these two-variable functions are convex on the coordinates. Finally, some applications for Simpson’s 3/8 cubature formula are given.

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 Some inequalities for double integrals and applications for cubature formula

2019 ◽  
Vol 11 (2) ◽  
pp. 271-295
Author(s):  
Samet Erden ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Numerical Analysis ◽  
Cubature Formula ◽  
Second Order ◽  
Absolute Value ◽  
Partial Derivatives ◽  
Double Integrals

Abstract We establish two Ostrowski type inequalities for double integrals of second order partial derivable functions which are bounded. Then, we deduce some inequalities of Hermite-Hadamard type for double integrals of functions whose partial derivatives in absolute value are convex on the co-ordinates on rectangle from the plane. Finally, some applications in Numerical Analysis in connection with cubature formula are given.

scholarly journals A new q-integral identity and estimation of its bounds involving generalized exponentially μ-preinvex functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Artion Kashuri ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Differentiable Function ◽  
Integral Identity ◽  
Second Order ◽  
Integral Inequalities ◽  
Absolute Value ◽  
Type Integral ◽  
Preinvex Functions

Abstract In the article, we introduce the generalized exponentially μ-preinvex function, derive a new q-integral identity for second order q-differentiable function, and establish several new q-trapezoidal type integral inequalities for the function whose absolute value of second q-derivative is exponentially μ-preinvex.

scholarly journals Simpson type integral inequalities for convex functions via Riemann-Liouville integrals

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4415-4420 ◽  
Author(s):  
Erhan Set ◽  
Ahmet Akdemir ◽  
Emin Özdemir
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Type Integral ◽  
Derivatives Of ◽  
New Inequalities

In this paper some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals. Also, by special selections of n, we give some reduced results.

scholarly journals Hermite-Hadamard Type Integral Inequalities for Functions Whose Second-Order Mixed Derivatives Are Coordinated(s,m)-P-Convex

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yu-Mei Bai ◽  
Shan-He Wu ◽  
Ying Wu
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Beta Function ◽  
Second Order ◽  
Integral Inequalities ◽  
Type Integral ◽  
Mixed Derivatives ◽  
Expression Form

We establish some new Hermite-Hadamard type integral inequalities for functions whose second-order mixed derivatives are coordinated(s,m)-P-convex. An expression form of Hermite-Hadamard type integral inequalities via the beta function and the hypergeometric function is also presented. Our results provide a significant complement to the work of Wu et al. involving the Hermite-Hadamard type inequalities for coordinated(s,m)-P-convex functions in an earlier article.

scholarly journals Second Order Perturbations of Elliptic Elements with Respect to the Initial Ones

1999 ◽  
Vol 172 ◽  
pp. 453-454
Author(s):  
F.J. Marco Castillo ◽  
M.J. Martínez Usó ◽  
J.A. López Ortí
Keyword(s):  
Quadratic Form ◽  
Second Order ◽  
Initial Instant ◽  
Orbital Elements ◽  
Partial Derivatives ◽  
Orbital Parameters ◽  
The Matrix ◽  
The Individual ◽  
Derivatives Of

AbstractThe following paper is devoted to the theoretical exposition of the obtention of second order perturbations of elliptic elements and is a follow-up of previous papers (Marco et al., 1996; Marco et al., 1997) where the hypothesis was made that the matrix of the partial derivatives of the orbital elements with respect to the initial ones is the identity matrix at the initial instant only. So, we must compute them through the integration of Lagrange planetary equations and their partial derivatives.Such developments have been applied to the individual corrections of orbits together with the correction of the reference system through the minimization of a quadratic form obtained from the linearized residual. In this state two new targets emerged: 1.To be sure that the most suitable quadratic form was to be considered.2.To provide a wider vision of the behavior of the different orbital parameters in time.Both aims may be accomplished through the consideration of the second order partial derivatives of the elliptic orbital elements with respect to the initial ones.

scholarly journals A perturbation scheme for obtaining partial derivatives of Love-wave group-velocity dispersion

1975 ◽  
Vol 65 (6) ◽  
pp. 1753-1760
Author(s):  
Dan Kosloff
Keyword(s):  
Group Velocity ◽  
Love Wave ◽  
Group Velocity Dispersion ◽  
Second Order ◽  
Wave Number ◽  
Perturbation Scheme ◽  
Wave Group ◽  
Partial Derivatives ◽  
Velocity Spectra ◽  
Derivatives Of

abstract A method is derived for obtaining partial derivatives of Love-wave group-velocity spectra for a layered medium using a second-order perturbation theory. These partials are a prerequisite for systematic inversion of group-velocity spectra but they are helpful as well in trial and error methods. Mathematically the equation of motion and boundary conditions for Love waves are a singular Sturm Liouville type eigenvalue problem. In the case of a fixed wave number, the eigenvalues are the negative of the square of the frequencies. Thus, by expressing the first- and second-order perturbations of the eigenvalues in terms of partial derivatives of the frequency with respect to the wave number and material parameters of the medium, one can relate these perturbations to group-velocity partials. The scheme should be relatively economical and easy to incorporate in Love-wave dispersion codes.

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