Lebesgue-stieltjes integral inequalities in several variables with retardation

1990 ◽  
Vol 100 (3) ◽  
pp. 231-243 ◽  
Author(s):  
Xureong Mao
Keyword(s):  
Integral Inequalities ◽  
Stieltjes Integral ◽  
Several Variables

scholarly journals Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Euclidean Space ◽  
Convex Functions ◽  
Convex Bodies ◽  
Integral Inequalities ◽  
Divergence Theorem ◽  
Several Variables ◽  
Type Integral ◽  
Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

scholarly journals Two Ostrowski type inequalities for the Stieltjes integral of monotonic functions

2007 ◽  
Vol 75 (2) ◽  
pp. 299-311 ◽  
Author(s):  
W.-S. Cheung ◽  
S. S. Dragomir
Keyword(s):  
Numerical Analysis ◽  
Trapezoidal Rule ◽  
Integral Inequalities ◽  
Stieltjes Integral ◽  
Hölder Continuous ◽  
Monotonic Functions ◽  
Dual Case

Two integral inequalities of Ostrowski type for the Stieltjes integral are given. The first is for monotonic integrators and Hölder continuous integrands while the second considers the dual case, that is, for monotonic integrands and Hölder continuous integrators. Applications for the mid-point inequality that are useful in the numerical analysis of Stieltjes integrals are exhibited. Some connections with the generalised trapezoidal rule are also presented.

scholarly journals A Unified Approach to Some Classes of Nonlinear Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Nurgali K. Ashirbayev ◽  
Józef Banaś ◽  
Raina Bekmoldayeva
Keyword(s):  
Integral Equations ◽  
Stieltjes Integral ◽  
View Point ◽  
Unified Approach ◽  
Nonlinear Integral Equations ◽  
Several Variables ◽  
Quadratic Integral ◽  
Function Of Two Variables ◽  
Fractional Orders ◽  
Quadratic Integral Equations

We are going to discuss some important classes of nonlinear integral equations such as integral equations of Volterra-Chandrasekhar type, quadratic integral equations of fractional orders, nonlinear integral equations of Volterra-Wiener-Hopf type, and nonlinear integral equations of Erdélyi-Kober type. Those integral equations play very significant role in applications to the description of numerous real world events. Our aim is to show that the mentioned integral equations can be treated from the view point of nonlinear Volterra-Stieltjes integral equations. The Riemann-Stieltjes integral appearing in those integral equations is generated by a function of two variables. The choice of a suitable generating function enables us to obtain various kinds of integral equations. Some results concerning nonlinear Volterra-Stieltjes integral equations in several variables will be also discussed.

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