scholarly journals A MAIN CLASS OF INTEGRAL INEQUALITIES WITH APPLICATIONS

2016 ◽  
Vol 21 (4) ◽  
pp. 569-584
Author(s):  
Mohammad Masjed-Jamei ◽  
Edward Omey ◽  
Sever S. Dragomir
Keyword(s):  
Quadrature Formula ◽  
Error Bounds ◽  
Integral Transforms ◽  
Integral Inequalities ◽  
Main Class

In this paper, we define some integral transforms and obtain suitable bounds for them in order to introduce a main class of integral inequalities including Ostrowski and Ostrowski-Gr¨uss inequalities and various kinds of new integral inequalities. In this sense, we also introduce a three point quadrature formula and obtain its error bounds.

scholarly journals A new Ostrowski type inequality for functions whose first derivatives are of bounded variation

2016 ◽  
Vol 2 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Bounded Variation ◽  
Quadrature Formula ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Ostrowski Type Inequality ◽  
Type Integral

Abstract In this paper, we establish some new Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation and quadrature formula is provided

scholarly journals Hermite-Hadamard Type Inequalities for Mtm-Preinvex Functions

2017 ◽  
Vol 58 (1) ◽  
pp. 77-96
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Quadrature Formula ◽  
Beta Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Left Hand ◽  
Special Means ◽  
Preinvex Functions

AbstractIn the present paper, the notion of MTm-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MTm-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MTm-preinvex functions via classical integrals and Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given. These results not only extend the results appeared in the literature (see [13]), but also provide new estimates on these types.

scholarly journals Error bounds for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 231-239 ◽  
Author(s):  
Ljubica Mihic ◽  
Aleksandar Pejcev ◽  
Miodrag Spalevic
Keyword(s):  
Weight Function ◽  
Quadrature Formula ◽  
Error Bounds ◽  
Analytic Functions ◽  
Remainder Term ◽  
Applied Mathematics ◽  
Maximum Modulus ◽  
End Points ◽  
The Third ◽  
Fourth Kind

For analytic functions the remainder terms of quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points -+1, for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where maximum modulus of the kernel is attained. The obtained values confirm the corresponding conjectured values given by Gautschi and Li in paper [The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points, Journal of Computational and Applied Mathematics 33 (1990) 315-329.]

scholarly journals Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions

2017 ◽  
Vol 3 (1) ◽  
pp. 102-115
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Quadrature Formula ◽  
Beta Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Left Hand ◽  
Type Integral ◽  
Preinvex Functions

Abstract In this paper, the notion of generalized (s; m; ξ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized (s; m; ξ)-preinvex functions along with beta function are given. Moreover, we establish some new Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions via classical and Riemann-Liouville fractional integrals. These results not only extend the results appeared in the literature (see [10],[11]), but also provide new estimates on these types. At the end, some conclusions are given.

scholarly journals Fractional trapezium-type inequalities for strongly exponentially generalized preinvex functions with applications

2020 ◽  
pp. 38-38
Author(s):  
Artion Kashuri ◽  
Themistocles Rassias
Keyword(s):  
Applied Sciences ◽  
Error Estimates ◽  
Quadrature Formula ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Trapezium Type ◽  
Type Integral ◽  
Preinvex Functions

The aim of this paper is to introduce a new extension of preinvexity called strongly exponentially generalized (m; !1; !2; h1; h2)-preinvexity. Some new integral inequalities of trapezium-type for strongly exponentially generalized (m; !1; !2; h1; h2)-preinvex functions with modulus c via Riemann-Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for strongly exponentially generalized (m; !1; !2; h1; h2)-preinvex functions with modulus c via general fractional integrals are obtained. We show that the class of strongly exponentially generalized (m; !1; !2; h1; h2)-preinvex functions with modulus c includes several other classes of preinvex functions. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.

ERROR ESTIMATES FOR A CLASS OF INTEGRAL AND DISCRETE TRANSFORMS

2000 ◽  
Vol 36 (3-4) ◽  
pp. 291-306
Author(s):  
P.E. Ricci ◽  
G. Mastroianni
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Error Estimates ◽  
Error Bounds ◽  
Integral Transforms ◽  
Theoretical Error ◽  
Fourier Trans ◽  
Discrete Transforms

We consider a class of integral transforms which generalize the classical Fourier Trans- form.We erive some theoretical error bounds for the corresponding approximate iscrete transforms,inclu ing the Discrete Fourier Transform.

scholarly journals Error bounds of Micchelli–Rivlin quadrature formula for analytic functions

2013 ◽  
Vol 169 ◽  
pp. 23-34 ◽  
Author(s):  
Aleksandar V. Pejčev ◽  
Miodrag M. Spalević
Keyword(s):  
Quadrature Formula ◽  
Error Bounds ◽  
Analytic Functions
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