Some new delay integral inequalities and their applications

Yuan, Zhulin; Yuan, Xingwei; Meng, Fanwei; Zhang, Hongxia

doi:10.1016/j.amc.2008.11.043

Cited by 24 publications

(11 citation statements)

References 9 publications

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“…Inequality is a useful tool for describing various of quantitative relations in the real world [24][25][26][27][28][29][30][31][32]. It plays important role in mathematics.…”

Section: Introductionmentioning

confidence: 99%

Evaluation Model and Approximate Solution to Inconsistent Max‐Min Fuzzy Relation Inequalities in P2P File Sharing System

Yang

2019

Complexity

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Considering the requirement of biggest download speed of the terminals, a BitTorrent-like Peer-to-Peer (P2P) file sharing system can be reduced into a system of max-min fuzzy relation inequalities. In this paper we establish an evaluation model by the satisfaction degree, for comparing two arbitrary potential solutions of such system. Besides, based on the evaluation model, concept of approximate solution is defined. It is indeed a potential solution with highest satisfaction degree. Furthermore, effective algorithm is developed for obtaining the approximate solutions to inconsistent system. Numerical examples are provided to illustrate our proposed model and algorithm.

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“…Inequality is a useful tool for describing various of quantitative relations in the real world [24][25][26][27][28][29][30][31][32]. It plays important role in mathematics.…”

Section: Introductionmentioning

confidence: 99%

Evaluation Model and Approximate Solution to Inconsistent Max‐Min Fuzzy Relation Inequalities in P2P File Sharing System

Yang

2019

Complexity

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“…Liang et al extend the study of Lazarević et al and Luo et al to study a second order–delayed system based on the notation of delayed matrix cosine/sine of a polynomial of degree. For more recent contributions, we refer the reader to several previous studies . However, to our best knowledge, finite‐time stability of oscillating systems with 2 delays have not been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

“…For more recent contributions, we refer the reader to several previous studies. [25][26][27][28][29][30][31][32][33][34][35] However, to our best knowledge, finite-time stability of oscillating systems with 2 delays have not been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time stability of a class of oscillating systems with two delays

Cao

Wang

2018

Math Methods in App Sciences

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In this paper, we study finite‐time stability of an oscillating system with 2 delays. To derive a bounded of state vector, we use a representation of explicit solution involving 2‐delayed matrix polynomial of 2 indices after deriving some fundamental estimates for such delayed matrix polynomial of 2 indices. A sufficient condition is given. Finally, an example is given to demonstrate the application of the main result.

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“…During the past decades, with the development of the theory of differential and integral equations, a lot of integral and difference inequalities, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein, have been discovered, which play an important role in the research of boundedness, global existence, stability of solutions of differential and integral equations as well as difference equations.…”

Section: Introductionmentioning

confidence: 99%

Gronwall–Bellman type nonlinear delay integral inequalities on time scales

Feng

Meng

Zheng

2011

Journal of Mathematical Analysis and Applications

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In this paper, some Gronwall-Bellman type nonlinear delay integral inequalities on time scales are established, which provide a handy tool in deriving boundedness of solutions of certain delay dynamic equations on time scales. Our results generalize some of the main results in Lipovan (2006) [1], Pachpatte (2000) [2], Ferreira and Torres (2009) [3], Zhang and Meng (2008) [4], Cheung and Ren (2006) [5], Kim (2009) [6], and some of our results unify continuous and discrete analysis in the literature.

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Some new delay integral inequalities and their applications

Cited by 24 publications

References 9 publications

Evaluation Model and Approximate Solution to Inconsistent Max‐Min Fuzzy Relation Inequalities in P2P File Sharing System

Evaluation Model and Approximate Solution to Inconsistent Max‐Min Fuzzy Relation Inequalities in P2P File Sharing System

Finite‐time stability of a class of oscillating systems with two delays

Gronwall–Bellman type nonlinear delay integral inequalities on time scales

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