scholarly journals Explicit bounds on Gamidov type integral

2006 ◽  
Vol 37 (1) ◽  
pp. 1-9 ◽  
Author(s):  
B. G. Pachpatte
Keyword(s):  
Upper Bounds ◽  
Integral Inequalities ◽  
Type Integral ◽  
Explicit Bounds ◽  
Discrete Analogues

The aim of this paper is to establish explicit upper bounds on certain Gamidov type integral inequalities which can be used as convenient tools in some applications. The discrete analogues and applications are given to illustrate the usefulness of one of our results.

scholarly journals New Explicit Bounds on Gamidov Type Integral Inequalities for Functions in Two Variables and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Kelong Cheng ◽  
Chunxiang Guo
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Integral Inequalities ◽  
Fredholm Integral Equations ◽  
Uniqueness Of Solutions ◽  
Fredholm Type ◽  
Type Integral ◽  
Explicit Bounds ◽  
Linear And Nonlinear

Some linear and nonlinear Gamidov type integral inequalities in two variables are established, which can give the explicit bounds on the solutions to a class of Volterra-Fredholm integral equations. Some examples of application are presented to show boundedness and uniqueness of solutions of a Volterra-Fredholm type integral equation.

scholarly journals Generalizations of Wendroff Integral Inequalities and Their Discrete Analogues

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Maksat Ashyraliyev
Keyword(s):  
Goursat Problem ◽  
Integral Inequalities ◽  
Stability Estimates ◽  
Type Integral ◽  
Discrete Analogues ◽  
The Stability

Generalizations of Wendroff type integral inequalities with four dependent limits and their discrete analogues are obtained. In applications, these results are used to establish the stability estimates for the solution of the Goursat problem.

scholarly journals ON SOME NEW GENERALIZATIONS OF CERTAIN GAMIDOV INTEGRAL INEQUALITIES IN TWO INDEPENDENT VARIABLES AND THEIR APPLICATIONS

2018 ◽  
pp. 467
Author(s):  
Khaled Boukerrioua ◽  
Dallel Diabi ◽  
Brahim Kilani
Keyword(s):  
Integral Inequalities ◽  
Independent Variables ◽  
Type Integral ◽  
Explicit Bounds ◽  
Two Independent Variables

The goal of this paper is to derive some new generalizations of certain Gamidov type integral inequalities in two variables which provide explicit bounds on unknown functions. To show the feasibility of the obtained inequalities,some illustrative examples are also introduce.

scholarly journals New Explicit Bounds on Gronwall-Bellman-Bihari-Gamidov Integral Inequalities and Their Weakly Singular Analogues with Applications

2020 ◽  
Vol 44 (4) ◽  
pp. 603-615
Author(s):  
M. MEKKI ◽  
K. BOUKERRIOUA ◽  
B. KILANI ◽  
M. L. SAHARI
Keyword(s):  
Integral Inequalities ◽  
Weakly Singular ◽  
Type Integral ◽  
Explicit Bounds

In this paper we derive some generalizations of certain Gronwall- Bellman-Bihari-Gamidov type integral inequalities and their weakly singular analogues, which provide explicit bounds on unknown functions. To show the feasibility of the obtained inequalities, two illustrative examples are also introduced.

Asymptotic behaviour of solutions of some general nonlinear differential equations and integral inequalities

1984 ◽  
Vol 98 (1-2) ◽  
pp. 49-67 ◽  
Author(s):  
Paul R. Beesack
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Nonlinear Differential Equations ◽  
Upper Bounds ◽  
Integral Inequalities ◽  
Asymptotic Behaviour Of Solutions ◽  
Type Integral ◽  
Image Position ◽  
Complex Valued

SynopsisWe deal with the asymptotic behaviour, as t→∞, of complex-valued solutions of nonlinear differential equationsUpper bounds for ∣x(l)(t)∣, 0≦j≦n, are obtained by obtaining upper bounds for solutions u(t) of Bihari-type integral inequalities of the form

scholarly journals On some useful integral inequalities and their discrete analogues

2002 ◽  
Vol 33 (2) ◽  
pp. 139-148
Author(s):  
S. B. Pachpatte ◽  
B. G. Pachpatte
Keyword(s):  
Integral Inequalities ◽  
Explicit Bounds ◽  
Discrete Analogues

In this paper explicit bounds on certain integral inequalities and their discrete analogues are established. To illustrate the usefulness of one of our results, some applications are also given.

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

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