一类非连续函数积分不等式中未知函数的估计及其应用

Abstract

Abstract:

In this paper we give the estimations of unknown functions of a class of integral inequalities for discontinuous functions by techniques of analysis and mathematical induction. Using our result we can solve the integral inequality for discontinuous function in[8]. We apply our result to a class of integral-differential equations with impulse perturbation for estimation.

Key words: Integral inequality for discontinuous function, Techniques , of , analysis, Mathematical induction, Estimation of unknown function

CLC Number:

34B15

LUO Ri-Cai, WANG Wu-Sheng, XU Hong-Lei. Estimation of Unknown Function of |a Class of Integral Inequalities for Discontinuous Function and its Application[J].Acta mathematica scientia,Series A, 2010, 30(4): 1176-1182.

Trendmd

References

[1] Agarwal R P, Deng S, Zhang W. Generalization of a retarded Gronwall-like inequality and its applications. Appl Math Comput, 2005, 165: 599--612

[2] Bainov D, Simeonov P. Integral Inequalities and Applications. Dordrecht: Kluwer Academic, 1992

[3] Bellman R. The stability of solutions of linear differential equations. Duke Math J, 1943, 10: 643--647

[4] Cs"orgo M, Révész P. Strong Approximations in Probability and Statistics. New York: Academic, 1981

[5] 陆传荣, 林正炎. 泛函型强不变原理. 中国科学, 1983, 11: 975--981

[6] Phillips P C B, Solo V. Asymptotic for linear processes. Ann Statist, 1992, 20: 971--1001

[7] Gronwall T H. Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann Math, 1919, 20: 292--296

[8] Iovane G. Some new integral inequalities of Bellman-Bihari type with delay for discontinuous functions. Nonlnear Anal, 2007, 66: 498--508

[9] Lipovan O. A retarded Gronwall-like inequality and its applications. J Math Anal Appl, 2000, 252: 389--401

[10] Mitrinovi'c D S, Pevcari'c J E, Fink A M. Inequalities Involving Functions and their Integrals and Derivatives. Dordrecht: Kluwer Academic, 1991

[11] Mitropolskiy Yu A, Iovane G, Borysenko S D. About a generalization of Bellman-Bihari type inequalities for discontinuous functions and their applications. Nonlnear Anal, 2007, 66: 2140--2165

[12] Ou-Yang L. The boundedness of solutions of linear differential equations y'' + A(t)y = 0. Shuxue Jinzhan, 1957, 3: 409--415

[13] Pachpatte B G. On some new inequalities related to certain inequalities in the theory of differential equations. J Math Anal Appl, 1995, 189: 128--144

[14] Pachpatte B G. Inequalities for Differential and Integral Equations. New York: Academic Press, 1998

[15] Wang W S. A generalized retarded Gronwall-like inequality in two variables and applications to BVP. Appl Math Comput, 2007, 191(1): 144--154

[16] 王五生. 一个推广的具有双重和离散不等式及其应用. 四川大学学报(自然科学版), 2007, 44(4): 733--738

[17] Wang W S, Shen C X. On a generalized retarded integral inequality with two variables. J Inequalities and Appl, 2008, 518646

[18] Wang W S. A generalized sum-difference inequality and applications to partial difference equations. Adv Difference Equ, 2008, 695495

{
[19] Zhang W, Deng S. Projected Gronwall-Bellman's inequality for integrable functions. Math Comput Modelling, 2001, 34: 394--402

Estimation of Unknown Function of |a Class of Integral Inequalities for Discontinuous Function and its Application

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0

[1]	Liu Huan, Wu Qiongli, Cournède Paul-Henry. Research on the Effects of Different Sampling Algorithm on Sobol Sensitivity Analysis [J]. Acta mathematica scientia,Series A, 2018, 38(2): 372-384.
[2]	Wang Shenghua, Cheng Guofei. The Asymptotic Behavior of the Solution in Structured Bacterial Population Model [J]. Acta mathematica scientia,Series A, 2018, 38(1): 156-167.
[3]	Wei Aiju, Zhang Xinjian, Wang Junyi, Li Kezan. Dynamics Analysis of an Ebola Epidemic Model [J]. Acta mathematica scientia,Series A, 2017, 37(3): 577-592.
[4]	Wang Shenghua, Wu Hongxing. Spectral Analysis of a Transport Operators in Rotenberg Model [J]. Acta mathematica scientia,Series A, 2016, 36(5): 821-831.
[5]	Wei Dongyi. Exact Number of Solutions of a One-Dimensional Prescribed Mean Curvature Equation with General Nonlinearities [J]. Acta mathematica scientia,Series A, 2016, 36(1): 1-13.
[6]	WANG Sheng-Hua, JIA Shan-De, YUAN Deng-Bin. Spectral Analysis of a Transport Operators in Cell Population [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1592-1598.
[7]	ZHANG Wei-Guo, LIU Qiang, LI Zheng-Ming, LI Xiang. BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT [J]. Acta mathematica scientia,Series A, 2014, 34(3): 941-959.
[8]	WEN Juan, HE Yin-Nian, WANG Xue-Min, HUO Mi-Hui. TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM [J]. Acta mathematica scientia,Series A, 2014, 34(3): 960-972.
[9]	CAI Dong-Han, YE Hui. Bifurcation and Multiple Growth Paths in an Economic Growth Model with Demographic Transition [J]. Acta mathematica scientia,Series A, 2014, 34(1): 9-15.
[10]	TAN Qiu-Heng, DING Yi-Ming. Empirical Analysis of Lottery Data Based on Non-stationarity Measure [J]. Acta mathematica scientia,Series A, 2014, 34(1): 207-216.
[11]	LV Xue-Bin, DAI Wan-Yang. Stochastic Integration for Fractional L\'{e}vy Processes and Stochastic Differential Equations Driven by Fractional L\'{e}vy Noises [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1022-1034.
[12]	WANG Sheng-Hua, CHENG Guo-Fei. Spectral Problem of \|Transport Equations with a Proliferating Cell Population [J]. Acta mathematica scientia,Series A, 2013, 33(1): 71-77.
[13]	ZENG Yun-Hui, LIN Lu, WANG Xiu-Li. Multi-Step-Adjustment Consistent Inference for Biased Sub-Model of Multidimensional Linear Regression [J]. Acta mathematica scientia,Series A, 2012, 32(6): 1019-1031.
[14]	SHI Ling, CHENG Xue-Guang. Scheduling a Single Server and Equal Processing Times in a Two-machine Flow-shop [J]. Acta mathematica scientia,Series A, 2012, 32(6): 1121-1125.
[15]	DAI Guo-Wei, WANG Wen-Ting, FENG Li-Li. Nonsmooth Version of Dual Fountain Theorem and Its Application to a Differential Inclusion Problem [J]. Acta mathematica scientia,Series A, 2012, 32(3): 530-539.