Fejér type inequalities for higher order convex functions and quadrature formulae

2021 ◽  
Author(s):  
J. Barić ◽  
Lj. Kvesić ◽  
J. Pečarić ◽  
M. Ribičić Penava
Keyword(s):  
Convex Functions ◽  
Higher Order ◽  
Quadrature Formulae

scholarly journals Hermite–Hadamard–Fejér-Type Inequalities and Weighted Three-Point Quadrature Formulae

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1720
Author(s):  
Mihaela Ribičić Penava
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Formula ◽  
Higher Order ◽  
Quadrature Formulae ◽  
Special Cases

The goal of this paper is to derive Hermite–Hadamard–Fejér-type inequalities for higher-order convex functions and a general three-point integral formula involving harmonic sequences of polynomials and w-harmonic sequences of functions. In special cases, Hermite–Hadamard–Fejér-type estimates are derived for various classical quadrature formulae such as the Gauss–Legendre three-point quadrature formula and the Gauss–Chebyshev three-point quadrature formula of the first and of the second kind.

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

scholarly journals Higher order strongly general convex functions and variational inequalities

2020 ◽  
Vol 5 (4) ◽  
pp. 3646-3663 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
◽  
Khalida Inayat Noor
Keyword(s):  
Variational Inequalities ◽  
Convex Functions ◽  
Higher Order ◽  
General Convex

scholarly journals Levinson type inequalities for higher order convex functions via Abel–Gontscharoff interpolation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Muhammad Adeel ◽  
Khuram Ali Khan ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Convex Functions ◽  
Higher Order ◽  
Data Points

Abstract In this paper, Levinson type inequalities are studied for the class of higher order convex functions by using Abel–Gontscharoff interpolation. Cebyšev, Grüss, and Ostrowski-type new bounds are also found for the functionals involving data points of two types.

Higher Order Strongly m-convex Functions

2021 ◽  
pp. 319-339
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Convex Functions ◽  
Higher Order
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