共查询到20条相似文献,搜索用时 15 毫秒
1.
Some continuous and discrete versions of Opial-type inequalities which are readily applicable to differential and difference operators are established. These generalize earlier results of Anastassiou and Pe?ari?, and of Koliha and Pe?ari?. 相似文献
2.
In this paper, some new discrete inequalities in two independent variables which provide explicit bounds on unknown functions are established. The inequalities given here can be used as tools in the qualitative theory of certain finite difference equations. 相似文献
3.
Some new explicit bounds on solutions to a class of new nonlinear Volterra–Fredholm-type discrete inequalities are established, which can be used as effective tools in the study of certain sum–difference equations. Application examples are also indicated. 相似文献
4.
In this article, we obtain some new nonlinear integral inequalities for discontinuous functions of two independent variables (Wendroff type) by including also inequalities with delay. We deduce new generalizations of earlier results given by R.P. Agarwal, R. Bellman, I. Bihari, B.K. Bondge, V. Lakshmikantham, S. Leela, B.G. Pachpatte for continuous and discrete functions. Furthermore, generalizations of some results for integro-sum inequalities are obtained as well. 相似文献
5.
Some new explicit bounds on solutions to a class of new nonlinear retarded Volterra–Fredholm type integral inequalities are established, which can be used as effective tools in the study of certain integral equations. Applications examples are also indicated. 相似文献
6.
The purpose of the present note is to establish some new delay integral inequalities, which provide explicit bounds on unknown functions and generalize some results of Li et al. [Some new delay integral inequalities and their applications, J. Comput. Appl. Math. 180 (2005) 191–200]. The inequalities given here can be used to investigate the qualitative properties of certain delay differential equations and delay integral equations. 相似文献
7.
J. Sándor 《Aequationes Mathematicae》1990,40(1):261-270
Summary Leta, b > 0 be positive real numbers. The identric meanI(a, b) of a andb is defined byI = I(a, b) = (1/e)(b
b
/a
a
)
1/(b–a)
, fora b, I(a, a) = a; while the logarithmic meanL(a, b) ofa andb isL = L(a, b) = (b – a)/(logb – loga), fora b, L(a, a) = a. Let us denote the arithmetic mean ofa andb byA = A(a, b) = (a + b)/2 and the geometric mean byG =G(a, b) =
. In this paper we obtain some improvements of known results and new inequalities containing the identric and logarithmic means. The material is divided into six parts. Section 1 contains a review of the most important results which are known for the above means. In Section 2 we prove an inequality which leads to some improvements of known inequalities. Section 3 gives an application of monotonic functions having a logarithmically convex (or concave) inverse function. Section 4 works with the logarithm ofI(a, b), while Section 5 is based on the integral representation of means and related integral inequalities. Finally, Section 6 suggests a new mean and certain generalizations of the identric and logarithmic means. 相似文献
8.
Suket Kumar 《Indagationes Mathematicae》2009,20(2):247-260
Necessary and sufficient conditions are given for a weighted norm inequality for the sum of two-dimensional Hardy-type integral operators with not necessarily non-negative coefficients. 相似文献
9.
A note on certain integral inequalities with delay 总被引:2,自引:0,他引:2
B. G. Pachpatte 《Periodica Mathematica Hungarica》1995,31(3):229-234
In this paper we establish some new integral inequalities with delay, which can be used as tools in the theory of some new classes of differential and integral equations. An application to obtain a bound on the solution of a certain integral equation is also given. 相似文献
10.
George A. Anastassiou 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5440-5445
Here we establish mixed Caputo fractional ‖.‖p, Landau type inequalities, p∈(1,∞]. We give applications on R. 相似文献
11.
B. G. Pachpatte 《Periodica Mathematica Hungarica》1987,18(2):137-141
In the present paper we establish two new integral inequalities similar to Opial's inequality in two independent variables. The inequalities established in this paper are similar to the analogues of Calvert's generalizations of Opial's inequality, in two independent variables and contains in the special case the analogue of Opial's inequality given by G. S. Yang in two independent variables. 相似文献
12.
Summary We investigate generalizations of the classical Jensen and Chebyshev inequalities. On one hand, we restrict the class of functions and on the other we enlarge the class of measures which are allowed. As an example, consider the inequality (J)(f(x) d) A (f(x) d, d d = 1. Iff is an arbitrary nonnegativeL
x
function, this holds if 0, is convex andA = 1. Iff is monotone the measure need not be positive for (J) to hold for all convex withA = 1. If has higher monotonicity, e.g., is also convex, then we get a version of (J) withA < 1 and measures that need not be positive. 相似文献
13.
Horst Alzer 《Aequationes Mathematicae》1988,36(2-3):246-250
Summary In this paper we prove the following:IfA
n
,G
n
andH
n
(resp.A
n
,G
n
andH
n
) denote the arithmetic, geometric and harmonic means ofa
1,, a
n
(resp. 1 –a
1,, 1 –a
n
) and ifa
i
(0, 1/2],i = 1,,n, then(G
n
/G
n
)
n
(A
n
/A
n
)
n-1
H
n
/H
n
, (*) with equality holding forn = 1,2. Forn 3 equality holds if and only ifa
1 = =a
n
. The inequality (*) sharpens the well-known inequality of Ky Fan:G
n
/G
n
A
n
/A
n
. 相似文献
14.
15.
16.
Wing-Sum Cheung 《Aequationes Mathematicae》1995,49(1):153-159
Summary In this paper some new integral inequalities of the Sobolev type involving many functions of many variables are established. These in turn can be used to serve as generators of other integral inequalities. 相似文献
17.
Qing-Hua Ma 《Journal of Computational and Applied Mathematics》2010,233(9):2170-2180
Some explicit bounds on solutions to a class of new power nonlinear Volterra-Fredholm type discrete inequalities are established, which can be used as effective tools in the study of certain sum-difference equations. Application examples are also given. 相似文献
18.
19.
In this article we present new integral Gronwall–Bellman–Bihari type inequalities for discontinuous functions (integro-sum inequalities). As applications, we investigate estimated solutions for impulsive differential systems, conditions of boundedness, stability, practical stability. 相似文献
20.
Michael Solomyak 《Integral Equations and Operator Theory》1994,19(1):120-124
This work was supported by a grant from the Minerva foundation. 相似文献