10 edition of **Some Gronwall Type Inequalities and Applications** found in the catalog.

- 345 Want to read
- 34 Currently reading

Published
**September 2003**
by Nova Science Publishers
.

Written in English

- Mathematics and Science,
- Science,
- Kernel functions,
- Mathematics,
- Science/Mathematics,
- Calculus,
- Gronwall inequalities,
- Research & Methodology,
- Differential equations

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 193 |

ID Numbers | |

Open Library | OL9435625M |

ISBN 10 | 1590338278 |

ISBN 10 | 9781590338278 |

OCLC/WorldCa | 52720655 |

inequalities. These inequalities involve Gronwall-Bellman type differential and integral inequalities [], retarded inequalities [], difference inequalities [], Volterra-Fredholm type inequalities [24,27], and dynamic inequal-ities on time scales []. Recently, some authors have researched and established some Gronwall-Bellman. During the past few years several authors (see references below and some of the references cited therein) have established several Gronwall type integral inequalities in one or two independent real variables -. Of course, such results have application in the theory of partial diﬀerential equations and Volterra integral equations.

Gronwall-Bellman type dynamic inequalities in t-wo independent variables on time scales contain-ing integration on inﬁnite intervals, which gener-alize the main results in [1] and [2], and present some applications for them. First we will give some preliminaries on calcu-lus of time scales and some universal symbols used in this paper. We establish some new integral inequalities of the Gronwall-Bellman-Reid type that have a wide range of applications to differential and integral equations. On inequalities of Gronwall-Bellman-Reid type II. Kuynkpook J. Math. v2.

Some New Discrete Gronwall-Bellman Type Inequalities with Three Independent Variables and Applications WeihuaLiu 1 andHaisongHuang 2 eralization of discrete Gronwall type inequalities in three independentvariablesineorem inthefollowing. eorem2. Let(,,) and (,,) bereal-valuednon-. scales. Some examples are considered to demonstrate the applications of the main results. Key words: Dynamic inequalities of Gronwall-Bellman Type, dy-namic equations, time scales. MSC (): 26D15, 26D20, 39A12, 34N 1 Introduction In Thomas Gronwall [8] proved that if β .

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Buy Some Gronwall Type Inequalities and Applications on FREE SHIPPING on qualified orders Some Gronwall Type Inequalities and Applications: Dragomir, Sever S.: : BooksCited by: Other Inequalities of Gronwall Type We will now present some other inequalities of Gronwall type that are known in the literature, by following the recent book of Mitrinovi´c, Peˇcari´c and.

Additional Physical Format: Online version: Dragomir, Sever Silvestru. Some gronwall type inequalities and applications. New York: Nova Science Publishers, © PDF | On Dec 7,Silvestru Sever and others published Some Gronwall type inequalities and applications | Find, read and cite all the research you need on ResearchGate.

Ostrowski type inequalities and applications in numerical Some Gronwall Type Inequalities and Applications book / edited by Sever S. Dragomir and Riemann-Stieltjes integral inequalities for complex functions defined on unit circle: with applications.

The purpose of this paper is to establish some new retarded integral inequalities of Gronwall-Bellman type, which generalizes some known integral inequalities. We use two lemmas to simplify the complex inequalities and give an upper bound estimation of the unknown function.

Therefore, our retarded Gronwall type inequalities is also interesting and important. Then, we derive two Henry–Gronwall type retarded integral inequalities. Furthermore, as some applications of these inequalities, certain properties of solutions to FDEs with delay are established. Henry–Gronwall type retarded integral inequalities.

Abstract. There are Gronwall type inequalities in which the unknown function is not a function on R n, rather in some other Chapter is devoted to these kinds; on. In this paper, some new nonlinear Gronwall-Bellman-type discrete inequalities are established, which can be used as a handy tool in the research of qualitative and quantitative properties of solutions of certain difference equations.

The established results generalize some of the recent results obtained by Cheung and Ma, respectively. Mathematics Subject Classification () 26D Advances in Mathematical Inequalities and Applications by Praveen Agarwal,available at Book Depository with free delivery worldwide.

We present several Gronwall-OuIang-type integral inequalities on time scales. Firstly, an OuIang inequality on time scales is discussed. Then we extend the Gronwall-type inequalities to multiple integrals. Some special cases of our results contain continuous Gronwall-type inequalities and their discrete analogues.

Several examples are included to illustrate our results at the end. This book concentrates on one- and multi-dimensional nonlinear integral and discrete Gronwall-Bellman type inequalities. It complements the author’s book on linear inequalities and serves as an essential tool for researchers interested in differential (ODE and PDE), difference, and integral equations.

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations.

In this paper, some nonlinear Gronwall–Bellman type inequalities are established. Then, the obtained results are applied to study the Hyers–Ulam stability of a fractional differential equation and the boundedness of solutions to an integral equation, respectively.

This paper is devoted to the study of Gronwall–Bellman-type inequalities on an arbitrary time scale T $\\mathbb{T}$. We investigate some new explicit bounds of a certain class of nonlinear retarded dynamic inequalities of Gronwall–Bellman type on time scales.

These inequalities extend some known dynamic inequalities on time scales. We also generalize and unify some continuous inequalities. Delay discrete inequalities with more than one nonlinear term are discussed, which generalize some known results and can be used in the analysis of various problems in the theory of certain classes of discrete equations.

Application examples to show boundedness and uniqueness of solutions of a Volterra type difference equation are also given. On some Gronwall-type integral inequalities in n independent variables, J.

Math. Anal. Appl. (), – MathSciNet zbMATH CrossRef Google Scholar In this paper, we study a certain class of nonlinear inequalities of Gronwall-Bellman type, which generalizes some known results and can be used as handy and effective tools in the study of differential equations and integral equations.

Furthermore, applications of our results to fractional differential are also involved. Preliminary Knowledge. Some new Gronwall–Ou-Iang type integral inequalities in two independent variables are established.

We also present some of its application to the study of. In this paper we established some vector-valued inequalities of Gronwall type in ordered Banach spaces. Our results can be applied to investigate systems of real-valued Gronwall-type inequalities.

We also show that the classical Gronwall-Bellman-Bihari integral inequality can be generalized from composition operators to a variety of operators, which include integral operators, maximal. Item Type: Book ISBN: Uncontrolled Keywords: ResPubID Gronwall, inequalities, applications: Subjects.Some new discrete inequalities of Gronwall – Bellman type that have a wide range of application in the theory of finite difference equations are given.

1. INTRODUCTION A powerful technique in the study of many problems concerning the behavior of solutions of discrete time systems.The goal of the present paper is to establish some new approach on the basic integral inequality of Gronwall-Bellman type and its generalizations involving function of one independent variable which provides explicit bounds on unknown functions.

The inequalities given here can be used as tools in the qualitative theory of certain partial differential and integral equations.