On quadratic integral inequalities associated with second-order symmetric differential expressions

1983 ◽  
pp. 170-223 ◽  
Author(s):  
W. N. Everitt ◽  
S. D. Wray
Keyword(s):  
Second Order ◽  
Integral Inequalities ◽  
Quadratic Integral

Some second-order integral inequalities of generalized Hardy type

1999 ◽  
Vol 129 (5) ◽  
pp. 947-958 ◽  
Author(s):  
B. Florkiewicz ◽  
K. Wojteczek
Keyword(s):  
Boundary Conditions ◽  
Second Order ◽  
Uniform Method ◽  
Integral Inequalities ◽  
Second Derivative ◽  
First Derivative ◽  
Hardy Type ◽  
Quadratic Integral

A uniform method of obtaining various types of integral inequalities involving a function and its first derivative is extended to integral inequalities involving a function and its second derivative. Specifically, some quadratic integral inequalities of generalized Hardy type involving a function and its second derivative are derived and examined. The functions for which the inequalities hold are characterized by boundary conditions.

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 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.

Lyapunov Type Integral Inequalities for Certain Differential Equations

1997 ◽  
Vol 4 (2) ◽  
pp. 139-148
Author(s):  
B. G. Pachpatte
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Second Order ◽  
Integral Inequalities ◽  
Asymptotic Behavior Of Solutions ◽  
Second Order Differential Equations ◽  
Elementary Analysis ◽  
Type Integral ◽  
Zeros Of Solutions

Abstract In the present paper we establish Lyapunov type integral inequalities related to the zeros of solutions of certain second-order differential equations by using elementary analysis. We also present some immediate applications of our results to study the asymptotic behavior of solutions of the corresponding differential equations.

scholarly journals Oscillation criteria for differential equations of second order

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
A. Nandakumaran ◽  
S. Panigrahi
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Integral Inequalities ◽  
Sufficient Condition ◽  
Oscillation Criteria ◽  
Oscillatory Nature ◽  
Non Linear

AbstractIn this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form $$ (r(t)y')' + q(t)y' + p(t)f(y)g(y') = 0, t \geqslant t_0 , $$ where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

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